Kamu tahu apa itu matriks? Di artikel Matematika kelas 11 ini, kita akan mengupas konsep matriks meliputi pengertian, jenis-jenis, serta transpose matriks. Simak baik-baik, ya!
—
Kamu pasti pernah menghadapi masalah yang berkaitan dengan angka dan data. Contoh kecilnya aja, saat kamu dan teman-temanmu lagi mau makan bersama. Biasanya kan, biar nggak ribet dan lupa, semua pesanan dicatat di kertas, ya. Tapi, kalo pesanannya banyak dan ribet, lumayan ngebingungin juga nggak sih nyatetnya mau gimana. Kayak yang waktu itu sempat ramai di sosial media, nih.
Perkara pesan nasi goreng (Sumber: suara.com)
Ya pantes abangnya nolak. Kamu aja yang sekali baca belum tentu paham. Iya apa iya? Ckckck… (geleng-geleng kelapa).
Sebenarnya, masalah di atas tuh bisa lho dibikin simpel dan gampang buat dipahami. Salah satunya pakai tabel. Nih, kalo aku buat ke dalam tabel, dengan barisnya menyatakan tingkat kepedasan dan kolomnya menyatakan telor, jadinya kayak gini.
Karena si sender nggak kasih keterangan tuh, pesanan nasi goreng yang telornya dicampur rasanya pedas atau nggak, jadi aku asumsiin aja rasanya sedang. Gimana, kalo dibuat tabel kayak gini, jadi jauh lebih gampang kan buat dimengerti sama abang nasi gorengnya? Hueheheheh 😛
Nah, kamu tau nggak sih, ternyata, tabel di atas bisa dibuat ke bentuk yang lebih sederhana lagi lho, yaitu seperti ini:
Urutan angka-angkanya sama. Cuma keterangan baris dan kolomnya aja yang dihilangkan. Terus, angka-angka tersebut diberi tanda kurung di sisi kanan dan kirinya. Kalo dalam Matematika, bentuk tersebut dinamakan matriks.
—
Sudah tahu belum, di Aplikasi belajar Ruangguru, ada fitur Drill Soal yang berisi kumpulan contoh soal latihan beserta pembahasannya, loh. Pas banget kan buat mempersiapkan diri kamu dalam menghadapi ujian nanti. Yuk, klik banner di bawah ini untuk coba fitur Drill Soal!
Matriks adalah sekumpulan bilangan yang disusun berdasarkan baris dan kolom, serta ditempatkan di dalam tanda kurung. Nah, tanda kurungnya ini bisa berupa kurung biasa “( )” atau kurung siku “[ ]”, ya. Suatu matriks diberi nama dengan huruf kapital, seperti A, B, C, dan seterusnya.
Oh iya, kamu tau kan bedanya baris dan kolom? Baris itu susunannya horizontal atau ke samping, sedangkan kolom susunannya vertikal atau dari atas ke bawah.
Misalnya nih, matriks di atas tadi, kita beri nama matriks A. Maka,
Penamaan baris dan kolom dibuat urut, ya. Jadi, baris ke-1 dimulai dari atas, urut ke bawah. Sementara itu, kolom ke-1 dimulai dari kiri ke kanan.
Baca Juga: Konsep Limit Fungsi Aljabar dan Sifat-sifatnya
Ordo dan Elemen Matriks
Matriks itu punya ukuran, guys. Ukuran matriks disebut ordo. Ordo matriks ini berdasarkan dari banyaknya baris dikali banyaknya kolom pada matriks. Jadi, kalo suatu matriks A memiliki m baris dan n kolom, maka matriks A tersebut berukuran (berordo) m x n. Supaya lebih sederhana, kita bisa menulisnya dengan Amxn.
Nah, masing-masing bilangan yang terdapat di dalam matriks disebut elemen matriks. Elemen-elemen matriks juga ada notasinya sendiri, lho. Kalo matriks dinotasikan dengan huruf kapital, maka elemen-elemen matriks dinotasikan dengan huruf kecil dan diberi indeks yang menyatakan letak baris dan kolomnya.
Misalnya nih, pada matriks A di atas, jumlah barisnya kan ada 5 dan jumlah kolomnya juga ada 5, maka ordonya adalah 5 x 5, atau bisa kita tulis A5×5. Lalu, untuk elemen-elemen matriks A bisa dinotasikan dengan aij, yang menyatakan elemen matriks A pada baris ke-i dan kolom ke-j.
Supaya kamu nggak bingung, langsung simak contoh di bawah ini aja, yuk!
Kita ambil contoh a11, a12, dan a54, seperti pada gambar.
- a11 menyatakan elemen matriks A pada baris ke-1 kolom ke-1, nilainya adalah 0.
- a12 menyatakan elemen matriks A pada baris ke-1 kolom ke-2, nilainya adalah 1.
- a54 menyatakan elemen matriks A pada baris ke-5 kolom ke-4, nilainya adalah 2.
Gimana, paham kan cara bacanya?
Baca Juga: Operasi Aljabar Pada Matriks: Penjumlahan, Pengurangan & Perkalian
—
Sebelum kita bahas tentang jenis-jenis matriks, kalo masih ada poin-poin yang belum kamu mengerti, mending belajar sama ahlinya, deh. Belajar bareng kakak-kakak pengajar di Ruangguru Privat Matematika misalnya.
Belajar nggak cuma menyenangkan, tapi kamu juga bakal diajari konsepnya sampai paham! Para pengajar di Ruangguru Privat juga sudah terstandarisasi kualitasnya, loh. Kamu juga bisa pilih nih, mau diajarkan secara langsung (offline) atau daring (online). Fleksibel, kan? Untuk info lebih lanjut, cuss klik link berikut!
Jenis-Jenis Matriks
Selain punya ukuran (ordo), matriks juga terbagi menjadi beberapa bentuk yang mempunyai sifat khusus. Nah, beberapa jenis matriks khusus yang perlu kamu ketahui di antaranya sebagai berikut:
a. Matriks Baris
Matriks baris adalah suatu matriks yang terdiri dari satu baris aja. Contoh matriks baris:
Kalo kita lihat, matriks A, matriks P, dan matriks Q, semuanya terdiri dari satu baris dan beberapa kolom. Untuk masing-masing ordonya, berarti A1×3, P1×4, dan Q1×5.
b. Matriks Kolom
Kebalikannya dari matriks baris, matriks kolom adalah suatu matriks yang terdiri dari satu kolom aja. Contoh matriks kolom:
Matriks R, matriks S, dan matriks T sama-sama terdiri dari satu kolom dan beberapa baris. Oleh karena itu, ordo matriksnya adalah R2×1, S3×1, dan T4×1.
c. Matriks Persegi
Matriks persegi adalah suatu matriks yang memiliki jumlah baris dan kolom sama. Itu tandanya, m = n. Karena jumlah baris dan kolomnya sama, maka ordo matriksnya bisa kita tulis menjadi n x n, atau matriks ordo n.
Pada matriks persegi, terdapat diagonal utama, yaitu elemen-elemen matriks yang letak barisnya sama dengan letak kolomnya. Selain diagonal utama, ada juga diagonal samping atau diagonal kedua. Kalo kita tarik garis di sepanjang diagonal utama matriks, maka diagonal samping ini berada di arah sebaliknya. Contoh matriks persegi:
Nah, berdasarkan contoh di atas, matriks A memiliki jumlah baris dan kolom yang sama karena matriks ini merupakan matriks persegi, yaitu sebanyak 2. Maka, matriks ini merupakan matriks berordo 2. Kemudian, elemen-elemen pada diagonal utamanya adalah 8 dan 7. Coba deh, kalo matriks B, ordo dan diagonal utamanya apa aja, nih? Jawab di kolom komentar, ya!
d. Matriks Diagonal
Matriks diagonal adalah matriks persegi yang elemen-elemen selain diagonal utamanya bernilai nol. Contoh matriks diagonal:
Kalo kita perhatikan gambar di atas, elemen-elemen pada diagonal utama matriks Q adalah 3, 8, dan 5. Nah, di luar diagonal utama, semua elemennya bernilai 0. Misalnya, elemen Q12 adalah 0, lalu elemen Q21 juga 0.
e. Matriks Identitas
Matriks identitas adalah matriks persegi yang semua elemen pada diagonal utamanya bernilai satu, sedangkan elemen lainnya bernilai nol. Umumnya, matriks identitas dinotasikan dengan I disertai dengan ordonya. Contoh matriks identitas:
f. Matriks Nol
Sesuai namanya, matriks nol adalah matriks yang semua elemennya bernilai nol. Matriks nol biasanya dinotasikan dengan huruf O disertai ordonya. Contoh matriks nol:
Transpose Matriks
Oke, setelah kamu tau pengertian dan jenis-jenis matriks, kita lanjut ke materi berikutnya ya, yaitu transpose matriks.
“Bentar, bentar. Minum dulu, gan!” (sumber: giphy.com)
Apa itu transpose matriks?
Transpose matriks adalah suatu matriks yang diperoleh dari hasil pertukaran antara elemen baris dan kolomnya. Jadi, elemen-elemen pada baris akan kita tukar menjadi elemen-elemen pada kolom, atau sebaliknya. Pasti kamu bingung, kan? HAHAHAHAHA…
Yauds, kita langsung simak contoh di bawah ini, deh. Misalnya, kita akan mentranspose matriks A dan B. Maka, matriks transposenya bisa dinotasikan dengan At dan Bt.
Baca Juga: Cara Mencari Determinan & Invers Matriks Beserta Contohnya
Nah, kalo kamu perhatikan kotak warna-warni pada matriks di atas, kamu pasti paham nih dengan polanya. Aku kasih contoh, ya. Coba kamu lihat matriks A dan At! Elemen-elemen baris ke-1 matriks At (yang di kotak merah), itu merupakan pertukaran dari elemen-elemen kolom ke-1 matriks A. Begitu juga dengan elemen-elemen baris ke-2 matriks At (yang di kotak biru), merupakan pertukaran dari elemen-elemen kolom ke-2 matriks A. Paham, ya?
Sekarang, coba kamu kerjakan contoh soal di bawah ini. Caranya sama kok kayak yang udah dijelasin sebelumnya.
Gimana, guys, udah paham dengan konsep matriks? Sebetulnya, matriks itu materi yang mudah lho, seru lagi! Matriks ini bisa digunakan untuk menyelesaikan masalah sistem persamaan yang memiliki lebih dari dua variabel dengan cepat. Dibandingkan kamu harus menggunakan metode substitusi atau eliminasi. Jadi, penting banget untuk memahami materi satu ini.
Kalo kamu merasa masih belum begitu paham dengan materi yang udah dijelaskan di artikel ini, kamu bisa coba tonton video penjelasan lengkapnya di ruangbelajar. Di sana, ada konsep kilatnya juga, lho! Membantu kamu lebih mudah memahami materi dalam waktu singkat. Yuk, buktikan sekarang!
Referensi:
Ari, R. Indriyastuti. (2012) Perspektif Matematika 3 untuk Kelas XII SMA dan MA Program Ilmu Pengetahuan Alam. PT Tiga Serangkai Pustaka Mandiri.
Sumber Foto:
Foto ‘WA Chat Pesan Nasi Goreng’ [Daring]. Tautan: https://www.suara.com/lifestyle/2021/01/06/122000/pesanan-nasi-goreng-terlalu-ribet-warganet-ini-bantu-buatkan-tabel-excel?page=all (Diakses: 7 Mei 2021)
GIF ‘Orang Minum’ [Daring]. Tautan: https://giphy.com/gifs/reaction-mood-etrntfDOQriFaBUJ7I (Diakses: 7 Mei 2021)
<!DOCTYPE html>
<html lang="en-US">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<meta author="viewport" content="Ruangguru Tech Team">
<title>Mengenal Matriks: Pengertian, Jenis, dan Transpose</title>
<link rel="shortcut icon" href="https://cdn-web-2.ruangguru.com/homepage-web/public/assets/icons/favicon.id.ico" type="image/x-icon" />
<!-- <link rel="profile" href="https://gmpg.org/xfn/11"> -->
<link rel="pingback" href="https://www.ruangguru.com/blog/xmlrpc.php">
<link rel="preconnect" href="https://fonts.googleapis.com">
<link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
<link href="https://fonts.googleapis.com/css2?family=Inter:wght@400;600;700&display=swap" rel="stylesheet">
<link rel="stylesheet" href="https://www.ruangguru.com/blog/wp-content/themes/ruangguru/css/bootstrap.min.css">
<link rel="stylesheet" href="https://www.ruangguru.com/blog/wp-content/themes/ruangguru/css/style.css">
<script src="https://www.ruangguru.com/blog/wp-content/themes/ruangguru/js/jquery-3.6.3.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/popper.js/1.16.0/umd/popper.min.js"></script>
<script src="https://www.ruangguru.com/blog/wp-content/themes/ruangguru/js/bootstrap.min.js"></script>
<script src="https://www.ruangguru.com/blog/wp-content/themes/ruangguru/js/main.js"></script>
<script src="https://www.ruangguru.com/blog/wp-content/themes/ruangguru/js/side-banner.js"></script>
<!-- Google Tag Manager -->
<meta name="google-site-verification" content="VJAn1g6wmtTZPpTXh-B4xoSFEkUi5jcV74xQSr6jnOM" />
<!-- <script>
document.querySelector('meta[name="author"]').setAttribute("content", "Ruangguru Tech Team");
</script> -->
<meta name="publisher" content="PT Ruang Raya Indonesia">
<!-- Google Tag Manager -->
<script>
(function(w, d, s, l, i) {
w[l] = w[l] || [];
w[l].push({
'gtm.start': new Date().getTime(),
event: 'gtm.js'
});
var f = d.getElementsByTagName(s)[0],
j = d.createElement(s),
dl = l != 'dataLayer' ? '&l=' + l : '';
j.async = true;
j.src =
'https://www.googletagmanager.com/gtm.js?id=' + i + dl;
f.parentNode.insertBefore(j, f);
})(window, document, 'script', 'dataLayer', 'GTM-PVNLZFT');
</script>
<!-- End Google Tag Manager -->
<meta name='robots' content='index, follow, max-image-preview:large, max-snippet:-1, max-video-preview:-1' />
<style>img:is([sizes="auto" i], [sizes^="auto," i]) { contain-intrinsic-size: 3000px 1500px }</style>
<!-- This site is optimized with the Yoast SEO plugin v25.9 - https://yoast.com/wordpress/plugins/seo/ -->
<meta name="description" content="Kamu tahu apa itu matriks? Kali ini, kita akan mengupas konsep matriks meliputi pengertian, jenis-jenis, serta transpose matriks. Simak baik-baik, ya!" />
<link rel="canonical" href="https://www.ruangguru.com/blog/mengenal-matriks-dalam-matematika-pengertian-jenis-dan-transpose" />
<meta property="og:locale" content="en_US" />
<meta property="og:type" content="article" />
<meta property="og:title" content="Mengenal Matriks: Pengertian, Jenis, dan Transpose" />
<meta property="og:description" content="Kamu tahu apa itu matriks? Kali ini, kita akan mengupas konsep matriks meliputi pengertian, jenis-jenis, serta transpose matriks. Simak baik-baik, ya!" />
<meta property="og:url" content="https://www.ruangguru.com/blog/mengenal-matriks-dalam-matematika-pengertian-jenis-dan-transpose" />
<meta property="og:site_name" content="Belajar Gratis di Rumah Kapan Pun! | Blog Ruangguru" />
<meta property="article:publisher" content="https://www.facebook.com/ruanggurucom/" />
<meta property="article:published_time" content="2026-01-26T03:00:00+00:00" />
<meta property="article:modified_time" content="2026-01-27T19:58:53+00:00" />
<meta name="author" content="Hani Ammariah" />
<meta name="twitter:card" content="summary_large_image" />
<meta name="twitter:creator" content="@ruangguru" />
<meta name="twitter:site" content="@ruangguru" />
<meta name="twitter:label1" content="Written by" />
<meta name="twitter:data1" content="Hani Ammariah" />
<meta name="twitter:label2" content="Est. reading time" />
<meta name="twitter:data2" content="10 minutes" />
<script type="application/ld+json" class="yoast-schema-graph">{"@context":"https://schema.org","@graph":[{"@type":"WebPage","@id":"https://www.ruangguru.com/blog/mengenal-matriks-dalam-matematika-pengertian-jenis-dan-transpose","url":"https://www.ruangguru.com/blog/mengenal-matriks-dalam-matematika-pengertian-jenis-dan-transpose","name":"Mengenal Matriks: Pengertian, Jenis, dan Transpose","isPartOf":{"@id":"https://www.ruangguru.com/blog/#website"},"primaryImageOfPage":{"@id":"https://www.ruangguru.com/blog/mengenal-matriks-dalam-matematika-pengertian-jenis-dan-transpose#primaryimage"},"image":{"@id":"https://www.ruangguru.com/blog/mengenal-matriks-dalam-matematika-pengertian-jenis-dan-transpose#primaryimage"},"thumbnailUrl":"https://cdn-web-2.ruangguru.com/landing-pages/assets/090bde7e-e7d3-42ff-a840-c2119499067c.png","datePublished":"2026-01-26T03:00:00+00:00","dateModified":"2026-01-27T19:58:53+00:00","author":{"@id":"https://www.ruangguru.com/blog/#/schema/person/9ba3cbf9caa7870d342cdec976efa08f"},"description":"Kamu tahu apa itu matriks? Kali ini, kita akan mengupas konsep matriks meliputi pengertian, jenis-jenis, serta transpose matriks. Simak baik-baik, ya!","breadcrumb":{"@id":"https://www.ruangguru.com/blog/mengenal-matriks-dalam-matematika-pengertian-jenis-dan-transpose#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https://www.ruangguru.com/blog/mengenal-matriks-dalam-matematika-pengertian-jenis-dan-transpose"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https://www.ruangguru.com/blog/mengenal-matriks-dalam-matematika-pengertian-jenis-dan-transpose#primaryimage","url":"https://cdn-web-2.ruangguru.com/landing-pages/assets/090bde7e-e7d3-42ff-a840-c2119499067c.png","contentUrl":"https://cdn-web-2.ruangguru.com/landing-pages/assets/090bde7e-e7d3-42ff-a840-c2119499067c.png"},{"@type":"BreadcrumbList","@id":"https://www.ruangguru.com/blog/mengenal-matriks-dalam-matematika-pengertian-jenis-dan-transpose#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https://www.ruangguru.com/blog"},{"@type":"ListItem","position":2,"name":"Mengenal Matriks: Pengertian, Jenis, dan Transpose | Matematika Kelas 11"}]},{"@type":"WebSite","@id":"https://www.ruangguru.com/blog/#website","url":"https://www.ruangguru.com/blog/","name":"Ruangguru Blog","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https://www.ruangguru.com/blog/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Person","@id":"https://www.ruangguru.com/blog/#/schema/person/9ba3cbf9caa7870d342cdec976efa08f","name":"Hani Ammariah","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https://www.ruangguru.com/blog/#/schema/person/image/","url":"https://secure.gravatar.com/avatar/d29c518b877e6defbe0f9758dd24fbdb1d812d0dd21801df009c62b494f27c79?s=96&d=mm&r=g","contentUrl":"https://secure.gravatar.com/avatar/d29c518b877e6defbe0f9758dd24fbdb1d812d0dd21801df009c62b494f27c79?s=96&d=mm&r=g","caption":"Hani Ammariah"},"description":"Content Performance Coordinator at Ruangguru. I like to write things that are useful and also not. But I hope, you can learn something from this post. ^^","url":"https://www.ruangguru.com/blog/author/hani-ammariah"}]}</script>
<!-- / Yoast SEO plugin. -->
<link rel="alternate" type="application/rss+xml" title="Belajar Gratis di Rumah Kapan Pun! | Blog Ruangguru » Mengenal Matriks: Pengertian, Jenis, dan Transpose | Matematika Kelas 11 Comments Feed" href="https://www.ruangguru.com/blog/mengenal-matriks-dalam-matematika-pengertian-jenis-dan-transpose/feed" />
<script type="text/javascript">
/* <![CDATA[ */
window._wpemojiSettings = {"baseUrl":"https:\/\/s.w.org\/images\/core\/emoji\/15.1.0\/72x72\/","ext":".png","svgUrl":"https:\/\/s.w.org\/images\/core\/emoji\/15.1.0\/svg\/","svgExt":".svg","source":{"concatemoji":"https:\/\/www.ruangguru.com\/blog\/wp-includes\/js\/wp-emoji-release.min.js?ver=6.8.1"}};
/*! This file is auto-generated */
!function(i,n){var o,s,e;function c(e){try{var t={supportTests:e,timestamp:(new Date).valueOf()};sessionStorage.setItem(o,JSON.stringify(t))}catch(e){}}function p(e,t,n){e.clearRect(0,0,e.canvas.width,e.canvas.height),e.fillText(t,0,0);var t=new Uint32Array(e.getImageData(0,0,e.canvas.width,e.canvas.height).data),r=(e.clearRect(0,0,e.canvas.width,e.canvas.height),e.fillText(n,0,0),new Uint32Array(e.getImageData(0,0,e.canvas.width,e.canvas.height).data));return t.every(function(e,t){return e===r[t]})}function u(e,t,n){switch(t){case"flag":return n(e,"\ud83c\udff3\ufe0f\u200d\u26a7\ufe0f","\ud83c\udff3\ufe0f\u200b\u26a7\ufe0f")?!1:!n(e,"\ud83c\uddfa\ud83c\uddf3","\ud83c\uddfa\u200b\ud83c\uddf3")&&!n(e,"\ud83c\udff4\udb40\udc67\udb40\udc62\udb40\udc65\udb40\udc6e\udb40\udc67\udb40\udc7f","\ud83c\udff4\u200b\udb40\udc67\u200b\udb40\udc62\u200b\udb40\udc65\u200b\udb40\udc6e\u200b\udb40\udc67\u200b\udb40\udc7f");case"emoji":return!n(e,"\ud83d\udc26\u200d\ud83d\udd25","\ud83d\udc26\u200b\ud83d\udd25")}return!1}function f(e,t,n){var r="undefined"!=typeof WorkerGlobalScope&&self instanceof WorkerGlobalScope?new OffscreenCanvas(300,150):i.createElement("canvas"),a=r.getContext("2d",{willReadFrequently:!0}),o=(a.textBaseline="top",a.font="600 32px Arial",{});return e.forEach(function(e){o[e]=t(a,e,n)}),o}function t(e){var t=i.createElement("script");t.src=e,t.defer=!0,i.head.appendChild(t)}"undefined"!=typeof Promise&&(o="wpEmojiSettingsSupports",s=["flag","emoji"],n.supports={everything:!0,everythingExceptFlag:!0},e=new Promise(function(e){i.addEventListener("DOMContentLoaded",e,{once:!0})}),new Promise(function(t){var n=function(){try{var e=JSON.parse(sessionStorage.getItem(o));if("object"==typeof e&&"number"==typeof e.timestamp&&(new Date).valueOf()<e.timestamp+604800&&"object"==typeof e.supportTests)return e.supportTests}catch(e){}return null}();if(!n){if("undefined"!=typeof Worker&&"undefined"!=typeof OffscreenCanvas&&"undefined"!=typeof URL&&URL.createObjectURL&&"undefined"!=typeof Blob)try{var e="postMessage("+f.toString()+"("+[JSON.stringify(s),u.toString(),p.toString()].join(",")+"));",r=new Blob([e],{type:"text/javascript"}),a=new Worker(URL.createObjectURL(r),{name:"wpTestEmojiSupports"});return void(a.onmessage=function(e){c(n=e.data),a.terminate(),t(n)})}catch(e){}c(n=f(s,u,p))}t(n)}).then(function(e){for(var t in e)n.supports[t]=e[t],n.supports.everything=n.supports.everything&&n.supports[t],"flag"!==t&&(n.supports.everythingExceptFlag=n.supports.everythingExceptFlag&&n.supports[t]);n.supports.everythingExceptFlag=n.supports.everythingExceptFlag&&!n.supports.flag,n.DOMReady=!1,n.readyCallback=function(){n.DOMReady=!0}}).then(function(){return e}).then(function(){var e;n.supports.everything||(n.readyCallback(),(e=n.source||{}).concatemoji?t(e.concatemoji):e.wpemoji&&e.twemoji&&(t(e.twemoji),t(e.wpemoji)))}))}((window,document),window._wpemojiSettings);
/* ]]> */
</script>
<style id='wp-emoji-styles-inline-css' type='text/css'>
img.wp-smiley, img.emoji {
display: inline !important;
border: none !important;
box-shadow: none !important;
height: 1em !important;
width: 1em !important;
margin: 0 0.07em !important;
vertical-align: -0.1em !important;
background: none !important;
padding: 0 !important;
}
</style>
<link rel='stylesheet' id='wp-block-library-css' href='https://www.ruangguru.com/blog/wp-includes/css/dist/block-library/style.min.css?ver=6.8.1' type='text/css' media='all' />
<style id='classic-theme-styles-inline-css' type='text/css'>
/*! This file is auto-generated */
.wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none}
</style>
<style id='global-styles-inline-css' type='text/css'>
:root{--wp--preset--aspect-ratio--square: 1;--wp--preset--aspect-ratio--4-3: 4/3;--wp--preset--aspect-ratio--3-4: 3/4;--wp--preset--aspect-ratio--3-2: 3/2;--wp--preset--aspect-ratio--2-3: 2/3;--wp--preset--aspect-ratio--16-9: 16/9;--wp--preset--aspect-ratio--9-16: 9/16;--wp--preset--color--black: #000000;--wp--preset--color--cyan-bluish-gray: #abb8c3;--wp--preset--color--white: #ffffff;--wp--preset--color--pale-pink: #f78da7;--wp--preset--color--vivid-red: #cf2e2e;--wp--preset--color--luminous-vivid-orange: #ff6900;--wp--preset--color--luminous-vivid-amber: #fcb900;--wp--preset--color--light-green-cyan: #7bdcb5;--wp--preset--color--vivid-green-cyan: #00d084;--wp--preset--color--pale-cyan-blue: #8ed1fc;--wp--preset--color--vivid-cyan-blue: #0693e3;--wp--preset--color--vivid-purple: #9b51e0;--wp--preset--gradient--vivid-cyan-blue-to-vivid-purple: linear-gradient(135deg,rgba(6,147,227,1) 0%,rgb(155,81,224) 100%);--wp--preset--gradient--light-green-cyan-to-vivid-green-cyan: linear-gradient(135deg,rgb(122,220,180) 0%,rgb(0,208,130) 100%);--wp--preset--gradient--luminous-vivid-amber-to-luminous-vivid-orange: linear-gradient(135deg,rgba(252,185,0,1) 0%,rgba(255,105,0,1) 100%);--wp--preset--gradient--luminous-vivid-orange-to-vivid-red: linear-gradient(135deg,rgba(255,105,0,1) 0%,rgb(207,46,46) 100%);--wp--preset--gradient--very-light-gray-to-cyan-bluish-gray: linear-gradient(135deg,rgb(238,238,238) 0%,rgb(169,184,195) 100%);--wp--preset--gradient--cool-to-warm-spectrum: linear-gradient(135deg,rgb(74,234,220) 0%,rgb(151,120,209) 20%,rgb(207,42,186) 40%,rgb(238,44,130) 60%,rgb(251,105,98) 80%,rgb(254,248,76) 100%);--wp--preset--gradient--blush-light-purple: linear-gradient(135deg,rgb(255,206,236) 0%,rgb(152,150,240) 100%);--wp--preset--gradient--blush-bordeaux: linear-gradient(135deg,rgb(254,205,165) 0%,rgb(254,45,45) 50%,rgb(107,0,62) 100%);--wp--preset--gradient--luminous-dusk: linear-gradient(135deg,rgb(255,203,112) 0%,rgb(199,81,192) 50%,rgb(65,88,208) 100%);--wp--preset--gradient--pale-ocean: linear-gradient(135deg,rgb(255,245,203) 0%,rgb(182,227,212) 50%,rgb(51,167,181) 100%);--wp--preset--gradient--electric-grass: linear-gradient(135deg,rgb(202,248,128) 0%,rgb(113,206,126) 100%);--wp--preset--gradient--midnight: linear-gradient(135deg,rgb(2,3,129) 0%,rgb(40,116,252) 100%);--wp--preset--font-size--small: 13px;--wp--preset--font-size--medium: 20px;--wp--preset--font-size--large: 36px;--wp--preset--font-size--x-large: 42px;--wp--preset--spacing--20: 0.44rem;--wp--preset--spacing--30: 0.67rem;--wp--preset--spacing--40: 1rem;--wp--preset--spacing--50: 1.5rem;--wp--preset--spacing--60: 2.25rem;--wp--preset--spacing--70: 3.38rem;--wp--preset--spacing--80: 5.06rem;--wp--preset--shadow--natural: 6px 6px 9px rgba(0, 0, 0, 0.2);--wp--preset--shadow--deep: 12px 12px 50px rgba(0, 0, 0, 0.4);--wp--preset--shadow--sharp: 6px 6px 0px rgba(0, 0, 0, 0.2);--wp--preset--shadow--outlined: 6px 6px 0px -3px rgba(255, 255, 255, 1), 6px 6px rgba(0, 0, 0, 1);--wp--preset--shadow--crisp: 6px 6px 0px rgba(0, 0, 0, 1);}:where(.is-layout-flex){gap: 0.5em;}:where(.is-layout-grid){gap: 0.5em;}body .is-layout-flex{display: flex;}.is-layout-flex{flex-wrap: wrap;align-items: center;}.is-layout-flex > :is(*, div){margin: 0;}body .is-layout-grid{display: grid;}.is-layout-grid > :is(*, div){margin: 0;}:where(.wp-block-columns.is-layout-flex){gap: 2em;}:where(.wp-block-columns.is-layout-grid){gap: 2em;}:where(.wp-block-post-template.is-layout-flex){gap: 1.25em;}:where(.wp-block-post-template.is-layout-grid){gap: 1.25em;}.has-black-color{color: var(--wp--preset--color--black) !important;}.has-cyan-bluish-gray-color{color: var(--wp--preset--color--cyan-bluish-gray) !important;}.has-white-color{color: var(--wp--preset--color--white) !important;}.has-pale-pink-color{color: var(--wp--preset--color--pale-pink) !important;}.has-vivid-red-color{color: var(--wp--preset--color--vivid-red) !important;}.has-luminous-vivid-orange-color{color: var(--wp--preset--color--luminous-vivid-orange) !important;}.has-luminous-vivid-amber-color{color: var(--wp--preset--color--luminous-vivid-amber) !important;}.has-light-green-cyan-color{color: var(--wp--preset--color--light-green-cyan) !important;}.has-vivid-green-cyan-color{color: var(--wp--preset--color--vivid-green-cyan) !important;}.has-pale-cyan-blue-color{color: var(--wp--preset--color--pale-cyan-blue) !important;}.has-vivid-cyan-blue-color{color: var(--wp--preset--color--vivid-cyan-blue) !important;}.has-vivid-purple-color{color: var(--wp--preset--color--vivid-purple) !important;}.has-black-background-color{background-color: var(--wp--preset--color--black) !important;}.has-cyan-bluish-gray-background-color{background-color: var(--wp--preset--color--cyan-bluish-gray) !important;}.has-white-background-color{background-color: var(--wp--preset--color--white) !important;}.has-pale-pink-background-color{background-color: var(--wp--preset--color--pale-pink) !important;}.has-vivid-red-background-color{background-color: var(--wp--preset--color--vivid-red) !important;}.has-luminous-vivid-orange-background-color{background-color: var(--wp--preset--color--luminous-vivid-orange) !important;}.has-luminous-vivid-amber-background-color{background-color: var(--wp--preset--color--luminous-vivid-amber) !important;}.has-light-green-cyan-background-color{background-color: var(--wp--preset--color--light-green-cyan) !important;}.has-vivid-green-cyan-background-color{background-color: var(--wp--preset--color--vivid-green-cyan) !important;}.has-pale-cyan-blue-background-color{background-color: var(--wp--preset--color--pale-cyan-blue) !important;}.has-vivid-cyan-blue-background-color{background-color: var(--wp--preset--color--vivid-cyan-blue) !important;}.has-vivid-purple-background-color{background-color: var(--wp--preset--color--vivid-purple) !important;}.has-black-border-color{border-color: var(--wp--preset--color--black) !important;}.has-cyan-bluish-gray-border-color{border-color: var(--wp--preset--color--cyan-bluish-gray) !important;}.has-white-border-color{border-color: var(--wp--preset--color--white) !important;}.has-pale-pink-border-color{border-color: var(--wp--preset--color--pale-pink) !important;}.has-vivid-red-border-color{border-color: var(--wp--preset--color--vivid-red) !important;}.has-luminous-vivid-orange-border-color{border-color: var(--wp--preset--color--luminous-vivid-orange) !important;}.has-luminous-vivid-amber-border-color{border-color: var(--wp--preset--color--luminous-vivid-amber) !important;}.has-light-green-cyan-border-color{border-color: var(--wp--preset--color--light-green-cyan) !important;}.has-vivid-green-cyan-border-color{border-color: var(--wp--preset--color--vivid-green-cyan) !important;}.has-pale-cyan-blue-border-color{border-color: var(--wp--preset--color--pale-cyan-blue) !important;}.has-vivid-cyan-blue-border-color{border-color: var(--wp--preset--color--vivid-cyan-blue) !important;}.has-vivid-purple-border-color{border-color: var(--wp--preset--color--vivid-purple) !important;}.has-vivid-cyan-blue-to-vivid-purple-gradient-background{background: var(--wp--preset--gradient--vivid-cyan-blue-to-vivid-purple) !important;}.has-light-green-cyan-to-vivid-green-cyan-gradient-background{background: var(--wp--preset--gradient--light-green-cyan-to-vivid-green-cyan) !important;}.has-luminous-vivid-amber-to-luminous-vivid-orange-gradient-background{background: var(--wp--preset--gradient--luminous-vivid-amber-to-luminous-vivid-orange) !important;}.has-luminous-vivid-orange-to-vivid-red-gradient-background{background: var(--wp--preset--gradient--luminous-vivid-orange-to-vivid-red) !important;}.has-very-light-gray-to-cyan-bluish-gray-gradient-background{background: var(--wp--preset--gradient--very-light-gray-to-cyan-bluish-gray) !important;}.has-cool-to-warm-spectrum-gradient-background{background: var(--wp--preset--gradient--cool-to-warm-spectrum) !important;}.has-blush-light-purple-gradient-background{background: var(--wp--preset--gradient--blush-light-purple) !important;}.has-blush-bordeaux-gradient-background{background: var(--wp--preset--gradient--blush-bordeaux) !important;}.has-luminous-dusk-gradient-background{background: var(--wp--preset--gradient--luminous-dusk) !important;}.has-pale-ocean-gradient-background{background: var(--wp--preset--gradient--pale-ocean) !important;}.has-electric-grass-gradient-background{background: var(--wp--preset--gradient--electric-grass) !important;}.has-midnight-gradient-background{background: var(--wp--preset--gradient--midnight) !important;}.has-small-font-size{font-size: var(--wp--preset--font-size--small) !important;}.has-medium-font-size{font-size: var(--wp--preset--font-size--medium) !important;}.has-large-font-size{font-size: var(--wp--preset--font-size--large) !important;}.has-x-large-font-size{font-size: var(--wp--preset--font-size--x-large) !important;}
:where(.wp-block-post-template.is-layout-flex){gap: 1.25em;}:where(.wp-block-post-template.is-layout-grid){gap: 1.25em;}
:where(.wp-block-columns.is-layout-flex){gap: 2em;}:where(.wp-block-columns.is-layout-grid){gap: 2em;}
:root :where(.wp-block-pullquote){font-size: 1.5em;line-height: 1.6;}
</style>
<link rel="https://api.w.org/" href="https://www.ruangguru.com/blog/wp-json/" /><link rel="alternate" title="JSON" type="application/json" href="https://www.ruangguru.com/blog/wp-json/wp/v2/posts/5041" /><link rel="EditURI" type="application/rsd+xml" title="RSD" href="https://www.ruangguru.com/blog/xmlrpc.php?rsd" />
<meta name="generator" content="WordPress 6.8.1" />
<link rel='shortlink' href='https://www.ruangguru.com/blog/?p=5041' />
<link rel="alternate" title="oEmbed (JSON)" type="application/json+oembed" href="https://www.ruangguru.com/blog/wp-json/oembed/1.0/embed?url=https%3A%2F%2Fwww.ruangguru.com%2Fblog%2Fmengenal-matriks-dalam-matematika-pengertian-jenis-dan-transpose" />
<link rel="alternate" title="oEmbed (XML)" type="text/xml+oembed" href="https://www.ruangguru.com/blog/wp-json/oembed/1.0/embed?url=https%3A%2F%2Fwww.ruangguru.com%2Fblog%2Fmengenal-matriks-dalam-matematika-pengertian-jenis-dan-transpose&format=xml" />
</head>
<body class="wp-singular post-template-default single single-post postid-5041 single-format-standard wp-theme-ruangguru">
<!-- Google Tag Manager (noscript) -->
<noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-M28L4XJ" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript>
<!-- End Google Tag Manager (noscript) -->
<header class="header">
<div class="container">
<nav class="navbar navbar-expand-lg header-inner">
<div style="display:flex; gap:12px;">
<button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbarSupportedContent" aria-controls="navbarSupportedContent" aria-expanded="false" aria-label="Toggle navigation">
<img alt="menu" src="https://cdn-web-2.ruangguru.com/file-uploader/lp/beba4a70-3971-41be-9364-f9ee6857b192.svg" loading="lazy" width="30px" height="32px" />
</button>
<a href="https://ruangguru.com" class="header-logo">
<img loading="lazy" src="https://cdn-web-2.ruangguru.com/static/logo-ruangguru.png" alt="Logo">
</a>
</div>
<form class="form-inline my-2 my-lg-0" role="search" method="get" id="searchformmobile" class="searchform" action="https://www.ruangguru.com/blog/">
<div>
<label class="screen-reader-text" for="s">Search for:</label>
<div class="input-group input-group-sm">
<span class="input-group-text" id="search-2"><img width="20px" height="20px" loading="lazy" src="https://cdn-web-2.ruangguru.com/file-uploader/lp/baf38d7b-226b-4374-8b2b-e49766395871.png" alt="" /></span>
<input type="text" value="" name="s" class="form-control" placeholder="Cari artikel di sini!" aria-label="Cari artikel di sini!" aria-describedby="Cari artikel di sini!">
</div>
</div>
</form>
<div class="collapse navbar-collapse dropdown-hover-all" id="navbarSupportedContent">
<div class="d-lg-none navbar-head-collapse">
<a href="https://ruangguru.com" class="header-logo">
<img loading="lazy" src="https://cdn-web-2.ruangguru.com/static/logo-ruangguru.png" alt="Logo">
</a>
<button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbarSupportedContent" aria-controls="navbarSupportedContent" aria-expanded="false" aria-label="Toggle navigation">
X
</button>
</div>
<ul class="navbar-nav me-auto mb-2 mb-lg-0">
<li class="nav-item">
<a class="nav-link" href="https://www.ruangguru.com/blog/">Blog</a>
</li>
<li class="nav-item
dropdown dropdown-hover">
<p class="nav-link dropdown-toggle" data-bs-toggle="dropdown" aria-haspopup="true" aria-expanded="false">
Konsep & Tips Pelajaran </p>
<div class="dropdown-menu" aria-labelledby="nav1">
<div class="dropdown dropend">
<a class="dropdown-item dropdown-toggle" id="nav1-menu0" href="https://www.ruangguru.com/blog/c/bahasa-indonesia" data-bs-toggle="dropdown" aria-haspopup="true" aria-expanded="false">Bahasa Indonesia</a>
<div class="dropdown-menu" aria-labelledby="nav1-menu0">
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/bahasa-indonesia/bahasa-indonesia-sd-kelas-4">Kelas 4</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/bahasa-indonesia/bahasa-indonesia-sd-kelas-5">Kelas 5</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/bahasa-indonesia/bahasa-indonesia-sd-kelas-6">Kelas 6</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/bahasa-indonesia/bahasa-indonesia-smp-kelas-7">Kelas 7</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/bahasa-indonesia/bahasa-indonesia-smp-kelas-8">Kelas 8</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/bahasa-indonesia/bahasa-indonesia-smp-kelas-9">Kelas 9</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/bahasa-indonesia/bahasa-indonesia-sma-kelas-10">Kelas 10</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/bahasa-indonesia/bahasa-indonesia-sma-kelas-11">Kelas 11</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/bahasa-indonesia/bahasa-indonesia-sma-kelas-12">Kelas 12</a>
</div>
</div>
<div class="dropdown dropend">
<a class="dropdown-item dropdown-toggle" id="nav1-menu1" href="https://www.ruangguru.com/blog/c/bahasa-inggris" data-bs-toggle="dropdown" aria-haspopup="true" aria-expanded="false">Bahasa Inggris</a>
<div class="dropdown-menu" aria-labelledby="nav1-menu1">
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/bahasa-inggris/bahasa-inggris-sd-kelas-6">Kelas 6</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/bahasa-inggris/bahasa-inggris-smp-kelas-7">Kelas 7</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/bahasa-inggris/bahasa-inggris-smp-kelas-8">Kelas 8</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/bahasa-inggris/bahasa-inggris-smp-kelas-9">Kelas 9</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/bahasa-inggris/bahasa-inggris-sma-kelas-10">Kelas 10</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/bahasa-inggris/bahasa-inggris-sma-kelas-11">Kelas 11</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/bahasa-inggris/bahasa-inggris-sma-kelas-12">Kelas 12</a>
</div>
</div>
<div class="dropdown dropend">
<a class="dropdown-item dropdown-toggle" id="nav1-menu2" href="https://www.ruangguru.com/blog/c/biologi" data-bs-toggle="dropdown" aria-haspopup="true" aria-expanded="false">Biologi</a>
<div class="dropdown-menu" aria-labelledby="nav1-menu2">
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/biologi/biologi-smp-kelas-7">Kelas 7</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/biologi/biologi-smp-kelas-8">Kelas 8</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/biologi/biologi-smp-kelas-9">Kelas 9</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/biologi/biologi-sma-kelas-10">Kelas 10</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/biologi/biologi-sma-kelas-11">Kelas 11</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/biologi/biologi-sma-kelas-12">Kelas 12</a>
</div>
</div>
<div class="dropdown dropend">
<a class="dropdown-item dropdown-toggle" id="nav1-menu3" href="https://www.ruangguru.com/blog/c/ekonomi" data-bs-toggle="dropdown" aria-haspopup="true" aria-expanded="false">Ekonomi</a>
<div class="dropdown-menu" aria-labelledby="nav1-menu3">
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/ekonomi/ekonomi-smp-kelas-7">Kelas 7</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/ekonomi/ekonomi-smp-kelas-8">Kelas 8</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/ekonomi/ekonomi-smp-kelas-9">Kelas 9</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/ekonomi/ekonomi-sma-kelas-10">Kelas 10</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/ekonomi/ekonomi-sma-kelas-11">Kelas 11</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/ekonomi/ekonomi-sma-kelas-12">Kelas 12</a>
</div>
</div>
<div class="dropdown dropend">
<a class="dropdown-item dropdown-toggle" id="nav1-menu4" href="https://www.ruangguru.com/blog/c/fisika" data-bs-toggle="dropdown" aria-haspopup="true" aria-expanded="false">Fisika</a>
<div class="dropdown-menu" aria-labelledby="nav1-menu4">
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/fisika/fisika-smp-kelas-7">Kelas 7</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/fisika/fisika-smp-kelas-8">Kelas 8</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/fisika/fisika-smp-kelas-9">Kelas 9</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/fisika/fisika-sma-kelas-10">Kelas 10</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/fisika/fisika-sma-kelas-11">Kelas 11</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/fisika/fisika-sma-kelas-12">Kelas 12</a>
</div>
</div>
<div class="dropdown dropend">
<a class="dropdown-item dropdown-toggle" id="nav1-menu5" href="https://www.ruangguru.com/blog/c/geografi" data-bs-toggle="dropdown" aria-haspopup="true" aria-expanded="false">Geografi</a>
<div class="dropdown-menu" aria-labelledby="nav1-menu5">
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/geografi/geografi-smp-kelas-7">Kelas 7</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/geografi/geografi-smp-kelas-8">Kelas 8</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/geografi/geografi-smp-kelas-9">Kelas 9</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/geografi/geografi-sma-kelas-10">Kelas 10</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/geografi/geografi-sma-kelas-11">Kelas 11</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/geografi/geografi-sma-kelas-12">Kelas 12</a>
</div>
</div>
<div class="dropdown dropend">
<a class="dropdown-item dropdown-toggle" id="nav1-menu6" href="https://www.ruangguru.com/blog/c/ipa-terpadu" data-bs-toggle="dropdown" aria-haspopup="true" aria-expanded="false">IPA Terpadu</a>
<div class="dropdown-menu" aria-labelledby="nav1-menu6">
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/ipa-terpadu/ipa-terpadu-sd-kelas-4">Kelas 4</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/ipa-terpadu/ipa-terpadu-sd-kelas-5">Kelas 5</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/ipa-terpadu/ipa-terpadu-sd-kelas-6">Kelas 6</a>
</div>
</div>
<div class="dropdown dropend">
<a class="dropdown-item dropdown-toggle" id="nav1-menu7" href="https://www.ruangguru.com/blog/c/ips-terpadu" data-bs-toggle="dropdown" aria-haspopup="true" aria-expanded="false">IPS Terpadu</a>
<div class="dropdown-menu" aria-labelledby="nav1-menu7">
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/ips-terpadu/ips-terpadu-sd-kelas-4">Kelas 4</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/ips-terpadu/ips-terpadu-sd-kelas-5">Kelas 5</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/ips-terpadu/ips-terpadu-sd-kelas-6">Kelas 6</a>
</div>
</div>
<div class="dropdown dropend">
<a class="dropdown-item dropdown-toggle" id="nav1-menu8" href="https://www.ruangguru.com/blog/c/kimia" data-bs-toggle="dropdown" aria-haspopup="true" aria-expanded="false">Kimia</a>
<div class="dropdown-menu" aria-labelledby="nav1-menu8">
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/kimia/kimia-sma-kelas-10">Kelas 10</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/kimia/kimia-sma-kelas-11">Kelas 11</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/kimia/kimia-sma-kelas-12">Kelas 12</a>
</div>
</div>
<div class="dropdown dropend">
<a class="dropdown-item dropdown-toggle" id="nav1-menu9" href="https://www.ruangguru.com/blog/c/matematika" data-bs-toggle="dropdown" aria-haspopup="true" aria-expanded="false">Matematika</a>
<div class="dropdown-menu" aria-labelledby="nav1-menu9">
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/matematika/matematika-sd-kelas-4">Kelas 4</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/matematika/matematika-sd-kelas-5">Kelas 5</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/matematika/matematika-sd-kelas-6">Kelas 6</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/matematika/matematika-smp-kelas-7">Kelas 7</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/matematika/matematika-smp-kelas-8">Kelas 8</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/matematika/matematika-smp-kelas-9">Kelas 9</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/matematika/matematika-sma-kelas-10">Kelas 10</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/matematika/matematika-sma-kelas-11">Kelas 11</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/matematika/matematika-sma-kelas-12">Kelas 12</a>
</div>
</div>
<div class="dropdown dropend">
<a class="dropdown-item dropdown-toggle" id="nav1-menu10" href="https://www.ruangguru.com/blog/c/sejarah" data-bs-toggle="dropdown" aria-haspopup="true" aria-expanded="false">Sejarah</a>
<div class="dropdown-menu" aria-labelledby="nav1-menu10">
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/sejarah/sejarah-smp-kelas-7">Kelas 7</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/sejarah/sejarah-smp-kelas-8">Kelas 8</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/sejarah/sejarah-smp-kelas-9">Kelas 9</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/sejarah/sejarah-sma-kelas-10">Kelas 10</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/sejarah/sejarah-sma-kelas-11">Kelas 11</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/sejarah/sejarah-sma-kelas-12">Kelas 12</a>
</div>
</div>
<div class="dropdown dropend">
<a class="dropdown-item dropdown-toggle" id="nav1-menu11" href="https://www.ruangguru.com/blog/c/sosiologi" data-bs-toggle="dropdown" aria-haspopup="true" aria-expanded="false">Sosiologi</a>
<div class="dropdown-menu" aria-labelledby="nav1-menu11">
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/sosiologi/sosiologi-smp-kelas-7">Kelas 7</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/sosiologi/sosiologi-smp-kelas-8">Kelas 8</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/sosiologi/sosiologi-smp-kelas-9">Kelas 9</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/sosiologi/sosiologi-sma-kelas-10">Kelas 10</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/sosiologi/sosiologi-sma-kelas-11">Kelas 11</a>
<a class="dropdown-item" href="https://www.ruangguru.com/blog/c/sosiologi/sosiologi-sma-kelas-12">Kelas 12</a>
</div>
</div>
</div>
</li>
<li class="nav-item
dropdown dropdown-hover">
<p class="nav-link dropdown-toggle" data-bs-toggle="dropdown" aria-haspopup="true" aria-expanded="false">
Latihan Soal </p>
<div class="dropdown-menu" aria-labelledby="nav2">
<a class="dropdown-item" id="nav2-menu0" href="https://www.ruangguru.com/blog/c/latihan-soal/sd-kelas-4">Latihan Soal Kelas 4</a>
<a class="dropdown-item" id="nav2-menu1" href="https://www.ruangguru.com/blog/c/latihan-soal/sd-kelas-5">Latihan Soal Kelas 5</a>
<a class="dropdown-item" id="nav2-menu2" href="https://www.ruangguru.com/blog/c/latihan-soal/sd-kelas-6">Latihan Soal Kelas 6</a>
<a class="dropdown-item" id="nav2-menu3" href="https://www.ruangguru.com/blog/c/latihan-soal/smp-kelas-7">Latihan Soal Kelas 7</a>
<a class="dropdown-item" id="nav2-menu4" href="https://www.ruangguru.com/blog/c/latihan-soal/smp-kelas-8">Latihan Soal Kelas 8</a>
<a class="dropdown-item" id="nav2-menu5" href="https://www.ruangguru.com/blog/c/latihan-soal/smp-kelas-9">Latihan Soal Kelas 9</a>
<a class="dropdown-item" id="nav2-menu6" href="https://www.ruangguru.com/blog/c/latihan-soal/sma-kelas-10">Latihan Soal Kelas 10</a>
<a class="dropdown-item" id="nav2-menu7" href="https://www.ruangguru.com/blog/c/latihan-soal/sma-kelas-11">Latihan Soal Kelas 11</a>
<a class="dropdown-item" id="nav2-menu8" href="https://www.ruangguru.com/blog/c/latihan-soal/sma-kelas-12">Latihan Soal Kelas 12</a>
</div>
</li>
<li class="nav-item
dropdown dropdown-hover">
<p class="nav-link dropdown-toggle" data-bs-toggle="dropdown" aria-haspopup="true" aria-expanded="false">
Pojok Kampus </p>
<div class="dropdown-menu" aria-labelledby="nav3">
<a class="dropdown-item" id="nav3-menu0" href="https://www.ruangguru.com/blog/c/info-beasiswa">Info Beasiswa</a>
<a class="dropdown-item" id="nav3-menu1" href="https://www.ruangguru.com/blog/c/kampus-dan-jurusan">Kampus dan Jurusan</a>
<a class="dropdown-item" id="nav3-menu2" href="https://www.ruangguru.com/blog/c/seleksi-masuk">Seleksi Masuk</a>
</div>
</li>
<li class="nav-item
">
<a class="nav-link
" href=" https://www.ruangguru.com/blog/c/fakta-seru" id="nav4"
>
Fakta Seru </a>
</li>
<li class="nav-item
dropdown dropdown-hover">
<p class="nav-link dropdown-toggle" data-bs-toggle="dropdown" aria-haspopup="true" aria-expanded="false">
Dunia Kata </p>
<div class="dropdown-menu" aria-labelledby="nav5">
<a class="dropdown-item" id="nav5-menu0" href="https://www.ruangguru.com/blog/tag/cerpen">Cerpen</a>
<a class="dropdown-item" id="nav5-menu1" href="https://www.ruangguru.com/blog/tag/resensi-buku">Resensi Buku</a>
</div>
</li>
<li class="nav-item
">
<a class="nav-link
" href=" https://www.ruangguru.com/blog/tag/for-kids" id="nav6"
>
For Kids </a>
</li>
<li class="nav-item
dropdown dropdown-hover">
<p class="nav-link dropdown-toggle" data-bs-toggle="dropdown" aria-haspopup="true" aria-expanded="false">
Seputar Ruangguru </p>
<div class="dropdown-menu" aria-labelledby="nav7">
<a class="dropdown-item" id="nav7-menu0" href="https://www.ruangguru.com/blog/tag/info-ruangguru">Info Ruangguru</a>
<a class="dropdown-item" id="nav7-menu1" href="https://www.ruangguru.com/blog/tag/siaran-pers">Siaran Pers</a>
<a class="dropdown-item" id="nav7-menu2" href="https://www.ruangguru.com/blog/tag/cerita-juara">Cerita Juara</a>
<a class="dropdown-item" id="nav7-menu3" href="https://www.ruangguru.com/blog/tag/seputar-guru">Seputar Guru</a>
<a class="dropdown-item" id="nav7-menu4" href="https://www.ruangguru.com/blog/tag/lifeatruangguru">Life at Ruangguru</a>
</div>
</li>
</ul>
<form class="form-inline my-2 my-lg-0" role="search" method="get" id="searchform" class="searchform" action="https://www.ruangguru.com/blog/">
<div>
<label class="screen-reader-text" for="s">Search for:</label>
<div class="input-group input-group-sm">
<span class="input-group-text" id="search-2"><img width="10" height="10" loading="lazy" src="https://cdn-web-2.ruangguru.com/file-uploader/lp/baf38d7b-226b-4374-8b2b-e49766395871.png" alt="" /></span>
<input type="text" value="" name="s" class="form-control" placeholder="Cari artikel di sini!" aria-label="Cari artikel di sini!" aria-describedby="Cari artikel di sini!">
</div>
</div>
</form>
</div>
</nav>
<script>
(function($bs) {
const CLASS_NAME = 'has-child-dropdown-show';
$bs.Dropdown.prototype.toggle = function(_orginal) {
return function() {
document.querySelectorAll('.' + CLASS_NAME).forEach(function(e) {
e.classList.remove(CLASS_NAME);
});
let dd = this._element.closest('.dropdown').parentNode.closest('.dropdown');
for (; dd && dd !== document; dd = dd.parentNode.closest('.dropdown')) {
dd.classList.add(CLASS_NAME);
}
return _orginal.call(this);
}
}($bs.Dropdown.prototype.toggle);
document.querySelectorAll('.dropdown').forEach(function(dd) {
dd.addEventListener('hide.bs.dropdown', function(e) {
if (this.classList.contains(CLASS_NAME)) {
this.classList.remove(CLASS_NAME);
e.preventDefault();
}
e.stopPropagation(); // do not need pop in multi level mode
});
});
// for hover
document.querySelectorAll('.dropdown-hover, .dropdown-hover-all .dropdown').forEach(function(dd) {
dd.addEventListener('mouseenter', function(e) {
let toggle = e.target.querySelector(':scope>[data-bs-toggle="dropdown"]');
if (!toggle.classList.contains('show')) {
$bs.Dropdown.getOrCreateInstance(toggle).toggle();
dd.classList.add(CLASS_NAME);
$bs.Dropdown.clearMenus(e);
}
});
dd.addEventListener('mouseleave', function(e) {
let toggle = e.target.querySelector(':scope>[data-bs-toggle="dropdown"]');
if (toggle.classList.contains('show')) {
$bs.Dropdown.getOrCreateInstance(toggle).toggle();
}
});
});
})(bootstrap);
$(document).ready(() => {
if ($(window).width() > 991) {
$("a[data-bs-toggle='dropdown']").click(function() {
window.location = $(this).attr('href');
});
}
})
</script>
</div>
</header>
<div class="main-content">
<div class="side-banner-mobile">
</div>
<div class="glider-navigation mobile">
<div role="tablist" class="dots" id="side-banner-mobile-dots"></div>
<div class="glider-button-navigation">
<button aria-label="Previous" class="glider-prev" id="side-banner-mobile-prev"><img src="https://cdn-web-2.ruangguru.com/landing-pages/assets/412de767-9fab-4a4e-9a21-09b7ac9c5f96.png"></button>
<button aria-label="Next" class="glider-next" id="side-banner-mobile-next">
<img src="https://cdn-web-2.ruangguru.com/landing-pages/assets/754b0134-4f20-4cdd-af8c-d5918044d734.png">
</button>
</div>
</div>
<div class="container">
<div class="row">
<div class="col-md-8 post">
<div class="content">
<nav aria-label="breadcrumb">
<ol class="breadcrumb">
<!-- Home Link -->
<li class="breadcrumb-item"><a href="https://www.ruangguru.com/blog">Home</a></li>
<!-- Categories -->
<li class="breadcrumb-item"><a href="https://www.ruangguru.com/blog/c/matematika">Matematika</a></li><li class="breadcrumb-item"><a href="https://www.ruangguru.com/blog/c/matematika/matematika-sma-kelas-11">Matematika SMA Kelas 11</a></li> </ol>
</nav>
<h1 class="content-title">
Mengenal Matriks: Pengertian, Jenis, dan Transpose | Matematika Kelas 11 </h1>
<div class="content-meta">
<p class="content-author"><a href="https://www.ruangguru.com/blog/author/hani-ammariah" class="">Hani Ammariah</a> </p>
<p class="content-info"><span>January 26, 2026 • </span> <span>7 minutes read</span></p>
<br />
</div>
<div class="content-body">
<p style="line-height: 1.5;"><span style="color: #000000;"><img decoding="async" class="aligncenter size-medium" src="https://cdn-web-2.ruangguru.com/landing-pages/assets/090bde7e-e7d3-42ff-a840-c2119499067c.png" alt="apa itu matriks" /></span></p>
<blockquote>
<p style="text-align: center;"><span style="font-size: 16px;"><em>Kamu tahu <strong>apa itu matriks?</strong> Di <strong><a href="https://www.ruangguru.com/blog/c/matematika/matematika-sma-kelas-11">artikel Matematika kelas 11</a></strong> ini, kita akan mengupas konsep matriks meliputi pengertian, jenis-jenis, serta transpose matriks. Simak baik-baik, ya!</em></span></p>
</blockquote>
<p style="text-align: center;">—</p>
<p> </p>
<p style="text-align: justify;">Kamu pasti pernah menghadapi masalah yang berkaitan dengan angka dan data. Contoh kecilnya aja, saat kamu dan teman-temanmu lagi mau makan bersama. Biasanya kan, biar nggak ribet dan lupa, semua pesanan dicatat di kertas, ya. Tapi, kalo pesanannya banyak dan ribet, lumayan ngebingungin juga nggak sih nyatetnya mau gimana. Kayak yang waktu itu sempat ramai di sosial media, nih.</p>
<p><img decoding="async" style="width: 413px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/nasi%20goreng.png" alt="nasi goreng" width="413" /></p>
<p style="text-align: center;"><em>Perkara pesan nasi goreng (Sumber: suara.com)</em></p>
<p> </p>
<p style="text-align: justify;">Ya pantes abangnya nolak. Kamu aja yang sekali baca belum tentu paham. Iya apa iya? Ckckck… (geleng-geleng kelapa).</p>
<p style="text-align: justify;">Sebenarnya, masalah di atas tuh bisa lho dibikin simpel dan gampang buat dipahami. Salah satunya pakai tabel. Nih, kalo aku buat ke dalam tabel, dengan barisnya menyatakan tingkat kepedasan dan kolomnya menyatakan telor, jadinya kayak gini.</p>
<p><img decoding="async" style="width: 550px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/tabel%20nasi%20goreng.png" alt="tabel nasi goreng" width="550" /></p>
<p> </p>
<p style="text-align: justify;">Karena si <em>sender</em> nggak kasih keterangan tuh, pesanan nasi goreng yang telornya dicampur rasanya pedas atau nggak, jadi aku asumsiin aja rasanya sedang. Gimana, kalo dibuat tabel kayak gini, jadi jauh lebih gampang kan buat dimengerti sama abang nasi gorengnya? Hueheheheh 😛</p>
<p style="text-align: justify;">Nah, kamu tau nggak sih, ternyata, tabel di atas bisa dibuat ke bentuk yang lebih sederhana lagi lho, yaitu seperti ini:</p>
<p><img decoding="async" style="width: 132px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/matriks%201-1.png" alt="matriks" width="132" /></p>
<p style="text-align: justify;">Urutan angka-angkanya sama. Cuma keterangan baris dan kolomnya aja yang dihilangkan. Terus, angka-angka tersebut diberi tanda kurung di sisi kanan dan kirinya. Kalo dalam Matematika, bentuk tersebut dinamakan <span style="font-weight: bold;">matriks</span>.</p>
<p style="text-align: center;">—</p>
<p style="text-align: center;"><em>Sudah tahu belum, di Aplikasi belajar Ruangguru, ada fitur Drill Soal yang berisi kumpulan contoh soal latihan beserta pembahasannya, loh. Pas banget kan buat mempersiapkan diri kamu dalam menghadapi ujian nanti. Yuk, klik banner di bawah ini untuk coba fitur Drill Soal! </em></p>
<p><a href="https://link.ruangguru.com/blPk/drillsoal18" target="_blank" rel="noopener"><img decoding="async" class="aligncenter" src="https://roboguru-forum-cdn.ruangguru.com/image/c2c1718a-346a-471a-b761-b0a50adcfa50.png" alt="Fitur Drill Soal Ruangguru" width="1023" /></a></p>
<p> </p>
<h2><span style="font-size: 18pt;">Pengertian Matriks</span></h2>
<p style="text-align: justify;">Matriks adalah <strong>sekumpulan bilangan yang disusun berdasarkan baris dan kolom, serta ditempatkan di dalam tanda kurung</strong>. Nah, tanda kurungnya ini bisa berupa kurung biasa “( )” atau kurung siku “[ ]”, ya. Suatu matriks diberi nama dengan huruf kapital, seperti A, B, C, dan seterusnya.</p>
<p style="text-align: justify;">Oh iya, kamu tau kan bedanya baris dan kolom? Baris itu susunannya horizontal atau ke samping, sedangkan kolom susunannya vertikal atau dari atas ke bawah.</p>
<p style="text-align: justify;">Misalnya nih, matriks di atas tadi, kita beri nama matriks A. Maka,</p>
<p style="text-align: justify;"><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/baris%20dan%20kolom%20matriks.jpg" alt="baris dan kolom matriks" width="600" /></p>
<p> </p>
<p>Penamaan baris dan kolom dibuat urut, ya. Jadi, baris ke-1 dimulai dari atas, urut ke bawah. Sementara itu, kolom ke-1 dimulai dari kiri ke kanan.</p>
<p><strong>Baca Juga: <a href="/blog/konsep-limit-fungsi-aljabar-dan-sifat-sifatnya" rel="noopener">Konsep Limit Fungsi Aljabar dan Sifat-sifatnya</a></strong></p>
<p> </p>
<h2><span style="font-size: 18pt;">Ordo dan Elemen Matriks</span></h2>
<p style="text-align: justify;">Matriks itu punya ukuran, <em>guys</em>. Ukuran matriks disebut <strong>ordo</strong>. Ordo matriks ini berdasarkan dari banyaknya baris dikali banyaknya kolom pada matriks. Jadi, kalo suatu matriks A memiliki m baris dan n kolom, maka matriks A tersebut berukuran (berordo) m x n. Supaya lebih sederhana, kita bisa menulisnya dengan A<sub>mxn</sub>.</p>
<p style="text-align: justify;">Nah, masing-masing bilangan yang terdapat di dalam matriks disebut <strong>elemen matriks</strong>. Elemen-elemen matriks juga ada notasinya sendiri, lho. Kalo matriks dinotasikan dengan huruf kapital, maka elemen-elemen matriks dinotasikan dengan huruf kecil dan diberi indeks yang menyatakan <span style="font-weight: bold;">letak baris dan kolomnya</span>.</p>
<p style="text-align: justify;">Misalnya nih, pada matriks A di atas, jumlah barisnya kan ada 5 dan jumlah kolomnya juga ada 5, maka ordonya adalah 5 x 5, atau bisa kita tulis A<sub>5×5</sub>. Lalu, untuk elemen-elemen matriks A bisa dinotasikan dengan a<sub>ij</sub>, yang menyatakan elemen matriks A pada baris ke-i dan kolom ke-j.</p>
<p style="text-align: justify;">Supaya kamu nggak bingung, langsung simak contoh di bawah ini aja, yuk!</p>
<p style="text-align: justify;"><img decoding="async" style="width: 211px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/matriks%202-1.png" alt="ordo dan elemen matriks" width="211" /></p>
<p> </p>
<p style="text-align: justify;">Kita ambil contoh a<sub>11</sub>, a<sub>12</sub>, dan a<sub>54</sub>, seperti pada gambar.</p>
<ul>
<li aria-level="1">a<sub>11</sub> menyatakan elemen matriks A pada baris ke-1 kolom ke-1, nilainya adalah 0.</li>
<li aria-level="1">a<sub>12</sub> menyatakan elemen matriks A pada baris ke-1 kolom ke-2, nilainya adalah 1.</li>
<li aria-level="1">a<sub>54</sub> menyatakan elemen matriks A pada baris ke-5 kolom ke-4, nilainya adalah 2.</li>
</ul>
<p> </p>
<p style="text-align: justify;">Gimana, paham kan cara bacanya?</p>
<p><strong>Baca Juga: <a href="https://www.ruangguru.com/blog/matematika-kelas-11-operasi-aljabar-pada-matriks-penjumlahan-pengurangan-dan-perkalian">Operasi Aljabar Pada Matriks: Penjumlahan, Pengurangan & Perkalian</a></strong></p>
<p style="text-align: center;">—</p>
<p style="text-align: justify;">Sebelum kita bahas tentang jenis-jenis matriks, kalo masih ada poin-poin yang belum kamu mengerti, mending belajar sama ahlinya, deh. Belajar bareng kakak-kakak pengajar di <a href="https://www.ruangguru.com/privat/matematika"><strong>Ruangguru Privat Matematika</strong></a> misalnya.</p>
<p style="text-align: justify;">Belajar nggak cuma menyenangkan, tapi kamu juga bakal diajari konsepnya sampai paham! Para pengajar di Ruangguru Privat juga sudah terstandarisasi kualitasnya, loh. Kamu juga bisa pilih nih, mau diajarkan secara langsung (<em>offline</em>) atau daring (<em>online</em>). Fleksibel, kan? Untuk info lebih lanjut, cuss klik link berikut!</p>
<p><a href="https://cta.ruangguru.com/blog-rg-10-privat-b?referrer=https%253A%252F%252Fwww.ruangguru.com%252Fblog%252Fpengenalan-istilah-statistik-data-tunggal-dalam-matematika&clientTimestamp=2026-01-27T19%3A57%3A26.495Z&cookiesId=961acec3-1a1e-4a64-944e-3848f02ffe14&sessionId=dae4c5cf-1cb3-4b48-a9f2-19449510ab38&clientDevice=Chrome+143+on+Windows+10&clientOS=Windows&clientOSVersion=10"><img decoding="async" class="aligncenter size-medium" src="https://cdn-web-2.ruangguru.com/landing-pages/assets/84b6f2c7-9c9c-480d-a218-7961334af9ce.png" alt="CTA Ruangguru Privat" /></a></p>
<p> </p>
<h2><span style="font-size: 18pt;">Jenis-Jenis Matriks</span></h2>
<p style="text-align: justify;">Selain punya ukuran (ordo), matriks juga terbagi menjadi beberapa bentuk yang mempunyai sifat khusus. Nah, beberapa jenis matriks khusus yang perlu kamu ketahui di antaranya sebagai berikut:</p>
<p> </p>
<h3><span style="font-size: 14pt;">a. Matriks Baris</span></h3>
<p style="text-align: justify;">Matriks baris adalah suatu matriks yang <strong>terdiri dari satu baris aja</strong>. Contoh matriks baris:</p>
<p style="text-align: justify;"><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/matriks%20baris.jpg" alt="matriks baris" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Kalo kita lihat, matriks A, matriks P, dan matriks Q, semuanya terdiri dari satu baris dan beberapa kolom. Untuk masing-masing ordonya, berarti A<sub>1×3</sub>, P<sub>1×4</sub>, dan Q<sub>1×5</sub>.</p>
<p> </p>
<h3><span style="font-size: 14pt;">b. Matriks Kolom</span></h3>
<p style="text-align: justify;">Kebalikannya dari matriks baris, matriks kolom adalah suatu matriks yang <strong>terdiri dari satu kolom aja</strong>. Contoh matriks kolom:</p>
<p style="text-align: justify;"><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/matriks%20kolom.jpg" alt="matriks kolom" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Matriks R, matriks S, dan matriks T sama-sama terdiri dari satu kolom dan beberapa baris. Oleh karena itu, ordo matriksnya adalah R<sub>2×1</sub>, S<sub>3×1</sub>, dan T<sub>4×1</sub>.</p>
<p> </p>
<h3><span style="font-size: 14pt;">c. Matriks Persegi</span></h3>
<p style="text-align: justify;">Matriks persegi adalah suatu matriks yang <strong>memiliki jumlah baris dan kolom sama</strong>. Itu tandanya, m = n. Karena jumlah baris dan kolomnya sama, maka ordo matriksnya bisa kita tulis menjadi n x n, atau matriks ordo n.</p>
<p style="text-align: justify;">Pada matriks persegi, terdapat <strong>diagonal utama</strong>, yaitu elemen-elemen matriks yang letak barisnya sama dengan letak kolomnya. Selain diagonal utama, ada juga diagonal samping atau diagonal kedua. Kalo kita tarik garis di sepanjang diagonal utama matriks, maka diagonal samping ini berada di arah sebaliknya. Contoh matriks persegi:</p>
<p style="text-align: justify;"><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/matriks%20persegi.jpg" alt="matriks persegi" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Nah, berdasarkan contoh di atas, matriks A memiliki jumlah baris dan kolom yang sama karena matriks ini merupakan matriks persegi, yaitu sebanyak 2. Maka, matriks ini merupakan matriks berordo 2. Kemudian, elemen-elemen pada diagonal utamanya adalah 8 dan 7. Coba deh, kalo matriks B, ordo dan diagonal utamanya apa aja, nih? Jawab di kolom komentar, ya!</p>
<p> </p>
<h3><span style="font-size: 14pt;">d. Matriks Diagonal</span></h3>
<p style="text-align: justify;">Matriks diagonal adalah <strong>matriks persegi yang</strong> <strong>elemen-elemen selain diagonal utamanya bernilai nol</strong>. Contoh matriks diagonal:</p>
<p style="text-align: justify;"><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/matriks%20diagonal.jpg" alt="matriks diagonal" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Kalo kita perhatikan gambar di atas, elemen-elemen pada diagonal utama matriks Q adalah 3, 8, dan 5. Nah, di <strong>luar</strong> diagonal utama, semua elemennya bernilai 0. Misalnya, elemen Q<sub>12</sub> adalah 0, lalu elemen Q<sub>21</sub> juga 0.</p>
<p> </p>
<h3><span style="font-size: 14pt;">e. Matriks Identitas</span></h3>
<p style="text-align: justify;">Matriks identitas adalah <strong>matriks persegi yang semua elemen pada diagonal utamanya bernilai satu, sedangkan elemen lainnya bernilai nol</strong>. Umumnya, matriks identitas dinotasikan dengan<em> I </em>disertai dengan ordonya. Contoh matriks identitas:</p>
<p style="text-align: justify;"><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/matriks%20identitas.jpg" alt="matriks identitas" width="600" /></p>
<p> </p>
<h3><span style="font-size: 14pt;">f. Matriks Nol</span></h3>
<p style="text-align: justify;">Sesuai namanya, matriks nol adalah <strong>matriks yang semua elemennya bernilai nol</strong>. Matriks nol biasanya dinotasikan dengan huruf O disertai ordonya. Contoh matriks nol:</p>
<p style="text-align: justify;"><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/contoh%20matriks%20nol.jpg" alt="contoh matriks nol" width="600" /></p>
<p> </p>
<h2><span style="font-size: 18pt;">Transpose Matriks</span></h2>
<p style="text-align: justify;">Oke, setelah kamu tau pengertian dan jenis-jenis matriks, kita lanjut ke materi berikutnya ya, yaitu transpose matriks.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 400px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/haus.gif" alt="haus" width="400" /></p>
<p style="text-align: center;"><em>“Bentar, bentar. Minum dulu, gan!” (sumber: giphy.com)</em></p>
<p> </p>
<p style="text-align: justify;">Apa itu transpose matriks?</p>
<p style="text-align: justify;">Transpose matriks adalah<strong> suatu matriks yang</strong> <strong>diperoleh dari hasil pertukaran antara elemen baris dan kolomnya</strong>. Jadi, elemen-elemen pada baris akan kita tukar menjadi elemen-elemen pada kolom, atau sebaliknya. Pasti kamu bingung, kan? HAHAHAHAHA…</p>
<p style="text-align: justify;"><span style="color: #000000;"><em>Yauds</em>, kita langsung simak contoh di bawah ini, deh. Misalnya, kita akan mentranspose matriks A dan B. Maka, matriks transposenya bisa dinotasikan dengan A<sup>t</sup> dan B<sup>t</sup>.</span></p>
<p><strong>Baca Juga: <a href="https://www.ruangguru.com/blog/cara-mencari-determinan-dan-invers-matriks">Cara Mencari Determinan & Invers Matriks Beserta Contohnya</a></strong></p>
<p style="text-align: justify;"><span style="color: #000000;"><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/transpose%20matriks.jpg" alt="transpose matriks" width="600" /></span></p>
<p> </p>
<p style="text-align: justify;">Nah, kalo kamu perhatikan kotak warna-warni pada matriks di atas, kamu pasti paham nih dengan polanya. Aku kasih contoh, ya. Coba kamu lihat matriks A dan A<sup>t</sup>! Elemen-elemen baris ke-1 matriks A<sup>t</sup> (yang di kotak merah), itu merupakan pertukaran dari elemen-elemen kolom ke-1 matriks A. Begitu juga dengan elemen-elemen baris ke-2 matriks A<sup>t</sup> (yang di kotak biru), merupakan pertukaran dari elemen-elemen kolom ke-2 matriks A. Paham, ya?</p>
<p style="text-align: justify;">Sekarang, coba kamu kerjakan contoh soal di bawah ini. Caranya sama kok kayak yang udah dijelasin sebelumnya.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/contoh%20soal%20matriks.png" alt="contoh soal matriks" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Gimana, <em>guys</em>, udah paham dengan konsep matriks? Sebetulnya, matriks itu materi yang mudah lho, seru lagi! Matriks ini bisa digunakan untuk menyelesaikan masalah sistem persamaan yang memiliki lebih dari dua variabel dengan cepat. Dibandingkan kamu harus menggunakan metode substitusi atau eliminasi. Jadi, penting banget untuk memahami materi satu ini.</p>
<p style="text-align: justify;">Kalo kamu merasa masih belum begitu paham dengan materi yang udah dijelaskan di artikel ini, kamu bisa coba tonton video penjelasan lengkapnya di <strong><a href="https://www.ruangguru.com/ruangbelajar" target="_blank" rel="noopener">ruangbelajar</a></strong>. Di sana, ada konsep kilatnya juga, lho! Membantu kamu lebih mudah memahami materi dalam waktu singkat. Yuk, buktikan sekarang!</p>
<p><a href="https://bayar.ruangguru.com/"><img decoding="async" class="aligncenter size-medium" src="https://cdn-web-2.ruangguru.com/landing-pages/assets/e3260f88-1749-4d3b-8973-be3aae07a94c.jpg" alt="CTA Ruangguru" /></a></p>
<p><strong>Referensi:</strong></p>
<p>Ari, R. Indriyastuti. (2012) Perspektif Matematika 3 untuk Kelas XII SMA dan MA Program Ilmu Pengetahuan Alam. PT Tiga Serangkai Pustaka Mandiri.</p>
<p><strong>Sumber Foto:</strong></p>
<p>Foto ‘WA Chat Pesan Nasi Goreng’ [Daring]. Tautan: https://www.suara.com/lifestyle/2021/01/06/122000/pesanan-nasi-goreng-terlalu-ribet-warganet-ini-bantu-buatkan-tabel-excel?page=all (Diakses: 7 Mei 2021)</p>
<p>GIF ‘Orang Minum’ [Daring]. Tautan: https://giphy.com/gifs/reaction-mood-etrntfDOQriFaBUJ7I (Diakses: 7 Mei 2021)</p>
</div>
<div class="content-meta-tags">
<a href="https://www.ruangguru.com/blog/tag/kelas-11" rel="tag">Kelas 11</a> <a href="https://www.ruangguru.com/blog/tag/konsep-pelajaran" rel="tag">Konsep Pelajaran</a> <a href="https://www.ruangguru.com/blog/tag/sma" rel="tag">SMA</a> </div>
</div>
<div class="author-post">
<img loading="lazy" class="author-avatar" width="64px" height="64px" src="https://cdn-web-2.ruangguru.com/landing-pages/assets/c67af191-a409-4002-8254-d4a3a5c1233c.jpg" alt="">
<div>
<h5 class="author-title">Hani Ammariah</h5>
<p class="author-description">Content Performance Coordinator at Ruangguru. I like to write things that are useful and also not. But I hope, you can learn something from this post. ^^</p>
</div>
</div> <div class="share-post">
<p>Bagikan artikel ini:</p>
<ul class="socmed">
<li>
<a target="_blank" href="https://api.whatsapp.com/send?phone=&text=Mengenal Matriks: Pengertian, Jenis, dan Transpose | Matematika Kelas 11%0D%0A%0D%0Ahttps://www.ruangguru.com/blog/mengenal-matriks-dalam-matematika-pengertian-jenis-dan-transpose"><img src="https://cdn-web-2.ruangguru.com/static/whatsapp.png" loading="lazy" alt="Logo Whatsapp " /></a>
</li>
<li>
<a target="_blank" href="https://www.facebook.com/share.php?u=https://www.ruangguru.com/blog/mengenal-matriks-dalam-matematika-pengertian-jenis-dan-transpose&quote=Mengenal Matriks: Pengertian, Jenis, dan Transpose | Matematika Kelas 11"> <img src="https://cdn-web-2.ruangguru.com/static/facebook.png" loading="lazy" alt="Logo Facebook " /> </a>
</li>
<li>
<a target="_blank" href="https://twitter.com/intent/tweet?text=Mengenal Matriks: Pengertian, Jenis, dan Transpose | Matematika Kelas 11&url=https://www.ruangguru.com/blog/mengenal-matriks-dalam-matematika-pengertian-jenis-dan-transpose"> <img src="https://cdn-web-2.ruangguru.com/static/twitter.png" loading="lazy" alt="Logo Twitter " /> </a>
</li>
<li>
<a target="_blank" href="https://www.linkedin.com/shareArticle?mini=true&url=https://www.ruangguru.com/blog/mengenal-matriks-dalam-matematika-pengertian-jenis-dan-transpose&title=Mengenal Matriks: Pengertian, Jenis, dan Transpose | Matematika Kelas 11"><img src="https://cdn-web-2.ruangguru.com/static/linkedin.png" loading="lazy" alt="Logo LinkedIn " /></a>
</li>
</ul>
</div>
</div>
<div class="col-md-4 sticky">
<aside id="sidebar">
<div class="side-banner-desktop">
</div>
<div class="glider-navigation desktop">
<div role="tablist" class="dots" id="side-banner-dots"></div>
<div class="glider-button-navigation">
<button aria-label="Previous" class="glider-prev" id="side-banner-prev"><img src="https://cdn-web-2.ruangguru.com/landing-pages/assets/412de767-9fab-4a4e-9a21-09b7ac9c5f96.png"></button>
<button aria-label="Next" class="glider-next" id="side-banner-next">
<img src="https://cdn-web-2.ruangguru.com/landing-pages/assets/754b0134-4f20-4cdd-af8c-d5918044d734.png">
</button>
</div>
</div>
<h2 style="font-size: 24px; font-weight: bold; margin-bottom: 16px;margin-top: 16px;">Artikel Terbaru</h2>
<ul>
<li>
<a href="https://www.ruangguru.com/blog/pergerakan-nasional-indonesia">
<img loading="lazy" src="https://cdn-web-2.ruangguru.com//landing-pages/assets/dd9f819a-e3e7-4992-b8c7-3ce436bb27f8.png" alt="Pergerakan Nasional" class="external-img wp-post-image " /> <span>Pergerakan Nasional Indonesia: Pengertian, Tujuan & Penyebabnya | Sejarah Kelas 11</span>
</a>
</li>
<li>
<a href="https://www.ruangguru.com/blog/runtuhnya-uni-soviet">
<img loading="lazy" src="https://cdn-web-2.ruangguru.com//landing-pages/assets/b9f1448f-d581-42c3-bf06-6300fdbcd7c8.png" alt="Runtuhnya Uni Soviet" class="external-img wp-post-image " /> <span>Sejarah Runtuhnya Uni Soviet, Penyebab, dan Dampaknya | Sejarah Kelas 12</span>
</a>
</li>
<li>
<a href="https://www.ruangguru.com/blog/konflik-palestina-israel">
<img loading="lazy" src="https://cdn-web-2.ruangguru.com//landing-pages/assets/724ad604-4b78-4c7c-9d4b-627165954c4a.png" class="external-img wp-post-image " /> <span>Latar Belakang Terjadinya Konflik Palestina dengan Israel | Sejarah Kelas 12</span>
</a>
</li>
<li>
<a href="https://www.ruangguru.com/blog/9-lembaga-dan-pelaku-pasar-modal-di-indonesia">
<img loading="lazy" src="https://cdn-web-2.ruangguru.com//landing-pages/assets/279825ac-672b-43f9-b66e-a1c7ec87f784.png" alt="Pelaku Pasar Modal di Indonesia" class="external-img wp-post-image " /> <span>9 Lembaga dan Pelaku Pasar Modal di Indonesia | Ekonomi Kelas 10</span>
</a>
</li>
<li>
<a href="https://www.ruangguru.com/blog/peristiwa-kontemporer-dunia-perpecahan-cekoslovakia">
<img loading="lazy" src="https://cdn-web-2.ruangguru.com//landing-pages/assets/2a1a35c0-f1f5-45d4-8869-ff5083bd90e5.png" alt="Perpecahan Cekoslowakia" class="external-img wp-post-image " /> <span>Latar Belakang Perpecahan Cekoslowakia dan Penyebabnya | Sejarah Kelas 12</span>
</a>
</li>
</ul>
</aside>
</div>
</div>
<div class="row">
<div class="col-12">
<section class="related-posts">
<h2 class="page-title">
Artikel Lainnya
</h2>
<div class="content-grid">
<div class="content">
<a href="https://www.ruangguru.com/blog/pergerakan-nasional-indonesia">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com//landing-pages/assets/dd9f819a-e3e7-4992-b8c7-3ce436bb27f8.png?height=320&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com//landing-pages/assets/dd9f819a-e3e7-4992-b8c7-3ce436bb27f8.png?height=320" type="image/png">
<img src="https://cdn-web-2.ruangguru.com//landing-pages/assets/dd9f819a-e3e7-4992-b8c7-3ce436bb27f8.png" loading="lazy" alt="" />
</picture>
<div>
<h2 class="content-title">
Pergerakan Nasional Indonesia: Pengertian, Tujuan & Penyebabnya | Sejarah Kelas 11 </h2>
<div class="content-meta">
<span>March 6, 2026</span> <span>• 8 minutes read</span>
</div>
</div>
</a>
</div>
<div class="content">
<a href="https://www.ruangguru.com/blog/runtuhnya-uni-soviet">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com//landing-pages/assets/b9f1448f-d581-42c3-bf06-6300fdbcd7c8.png?height=320&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com//landing-pages/assets/b9f1448f-d581-42c3-bf06-6300fdbcd7c8.png?height=320" type="image/png">
<img src="https://cdn-web-2.ruangguru.com//landing-pages/assets/b9f1448f-d581-42c3-bf06-6300fdbcd7c8.png" loading="lazy" alt="" />
</picture>
<div>
<h2 class="content-title">
Sejarah Runtuhnya Uni Soviet, Penyebab, dan Dampaknya | Sejarah Kelas 12 </h2>
<div class="content-meta">
<span></span> <span>• 11 minutes read</span>
</div>
</div>
</a>
</div>
<div class="content">
<a href="https://www.ruangguru.com/blog/konflik-palestina-israel">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com//landing-pages/assets/724ad604-4b78-4c7c-9d4b-627165954c4a.png?height=320&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com//landing-pages/assets/724ad604-4b78-4c7c-9d4b-627165954c4a.png?height=320" type="image/png">
<img src="https://cdn-web-2.ruangguru.com//landing-pages/assets/724ad604-4b78-4c7c-9d4b-627165954c4a.png" loading="lazy" alt="" />
</picture>
<div>
<h2 class="content-title">
Latar Belakang Terjadinya Konflik Palestina dengan Israel | Sejarah Kelas 12 </h2>
<div class="content-meta">
<span>March 5, 2026</span> <span>• 5 minutes read</span>
</div>
</div>
</a>
</div>
</div>
</section> </div>
</div>
<div class="banner-product-wrapper">
<a href="https://cta.ruangguru.com/7c02db90-610d-11ee-80fe-4201ac180089" target="_blank" class="alert alert-dismissible fade show banner-product" role="alert">
<button type="button" class="btn-close" data-bs-dismiss="alert" aria-label="Close"></button>
<!-- <p>Yuk pilih kelas dan materi belajar kamu di sini</p>
<img src="https://cdn-web-2.ruangguru.com/landing-pages/assets/0e292531-9ee1-4eed-92f5-b5c053eea4c2.svg" width="42px" height="42px" class="arrow-right"> -->
<img class="image-floating-bottom" src="https://cdn-web-2.ruangguru.com/landing-pages/assets/d19eb9b6-999d-4b92-87c6-c4fb32000d73.png?convert=web" />
</a>
</div>
</div>
</div>
<script>
function sleep(ms) {
return new Promise((resolve) => setTimeout(resolve, ms));
}
async function replaceCtaMarkupAsync() {
await sleep(2000);
alert("replace")
const contentBody = document.querySelector('.content-body');
const paragraphs = contentBody.querySelectorAll('p');
const regexPattern = /{{cta\(['"](.+?)['"]\)}}/g;
paragraphs.forEach((paragraph) => {
const originalHTML = paragraph.innerHTML;
let modifiedHTML = '';
let lastIndex = 0;
for (const match of originalHTML.matchAll(regexPattern)) {
const ctaId = match[1];
modifiedHTML += originalHTML.slice(lastIndex, match.index) + `<b>${ctaId}</b>`;
lastIndex = match.index + match[0].length;
}
modifiedHTML += originalHTML.slice(lastIndex);
paragraph.innerHTML = modifiedHTML;
});
document.addEventListener("DOMContentLoaded", () => {
replaceCtaMarkupAsync();
});
}
</script>
<div class="modal fade" id="popupPromo" tabindex="-1" aria-labelledby="popupPromoLabel" aria-hidden="true">
<div class="modal-dialog modal-dialog-centered" data-bs-backdrop="static" data-bs-keyboard="false">
<div class="modal-content">
<div class="button-wrapper">
<button type="button" class="btn-close" data-bs-dismiss="modal" aria-label="Close"></button>
</div>
<div class="glider-contain">
<div class="glider">
<a class="" target="_blank" href="https://cta.ruangguru.com/ab-web-pop-up-banner-blog-rg">
<img src="https://cdn-web-2.ruangguru.com//landing-pages/assets/4680961a-4e01-4169-8ff4-da0823d0da6c.png" />
</a>
<a class="" target="_blank" href="https://cta.ruangguru.com/ab-web-pop-up-banner-blog-rg-1">
<img src="https://cdn-web-2.ruangguru.com/landing-pages/assets/e0ebb0c9-e368-4524-9241-dbaf73cafccd.png" />
</a>
<a class="" target="_blank" href="https://cta.ruangguru.com/rasionalisasi-popup-blog-rg">
<img src="https://cdn-web-2.ruangguru.com/landing-pages/assets/0ec15e92-707a-4660-8134-11f1c1e539a8.png" />
</a>
<a class="" target="_blank" href="https://cta.ruangguru.com/to-snbt-reg-2026-popup-blog-rg">
<img src="https://cdn-web-2.ruangguru.com/landing-pages/assets/b95e02b2-28a4-4c24-a6db-930ecddef2fa.jpg" />
</a>
<a class="" target="_blank" href="https://cta.ruangguru.com/pop-blog-to-snbt-prem">
<img src="https://cdn-web-2.ruangguru.com//landing-pages/assets/1b8558a2-ad51-4144-b30c-01a3231a22da.jpg" />
</a>
<a class="" target="_blank" href="https://cta.ruangguru.com/to-prem-tka-sd-smp-popup-blog-rg">
<img src="https://cdn-web-2.ruangguru.com//landing-pages/assets/e6888a56-1d95-4d8a-b87a-b19b8a185651.png" />
</a>
<a class="" target="_blank" href="https://cta.ruangguru.com/rgp-popup-blog-rg">
<img src="https://cdn-web-2.ruangguru.com/landing-pages/assets/851003e6-07b5-40d1-9068-f9b0bcb1625a.png" />
</a>
<a class="" target="_blank" href="https://cta.ruangguru.com/25f78174-4fc2-11ef-9a39-4201ac180089">
<img src="https://cdn-web-2.ruangguru.com//landing-pages/assets/cbe7b869-fbe2-4497-8a1e-42344df5b137.jpg" />
</a>
<a class="" target="_blank" href="https://cta.ruangguru.com/kitab-tka-smp-popup-blog">
<img src="https://cdn-web-2.ruangguru.com//landing-pages/assets/eb41ad00-e4dc-46f5-b9f6-721266fc371e.jpg" />
</a>
<a class="" target="_blank" href="https://cta.ruangguru.com/pop-rg-kitab-utbk-snbt-lite">
<img src="https://cdn-web-2.ruangguru.com/landing-pages/assets/f7908ac1-3b0b-492c-bf87-dcea2b20b87c.png" />
</a>
<a class="" target="_blank" href="https://cta.ruangguru.com/pop-rg-kitablitetkasmp">
<img src="https://cdn-web-2.ruangguru.com/landing-pages/assets/50097055-1862-46a8-bbe0-fa5b077f88bb.png" />
</a>
</div>
<div class="glider-navigation">
<div role="tablist" class="dots" id="popup-promo-dots"></div>
<div class="glider-button-navigation">
<button aria-label="Previous" class="glider-prev" id="popup-promo-prev"><img src="https://cdn-web-2.ruangguru.com/landing-pages/assets/412de767-9fab-4a4e-9a21-09b7ac9c5f96.png"></button>
<button aria-label="Next" class="glider-next" id="popup-promo-next">
<img src="https://cdn-web-2.ruangguru.com/landing-pages/assets/754b0134-4f20-4cdd-af8c-d5918044d734.png">
</button>
</div>
</div>
</div>
</div>
</div>
</div>
<script>
var jsonString = '[{"CreatedAt":"2025-07-25 01:01:27+00:00","Id":696,"UpdatedAt":"2026-02-25 02:12:12+00:00","campaign":null,"cta":[{"Id":31467,"ctaId":"ab-web-pop-up-banner-blog-rg","ctaLink":"URI::(https:\/\/cta.ruangguru.com\/ab-web-pop-up-banner-blog-rg)","imageUrl":"https:\/\/cdn-web-2.ruangguru.com\/landing-pages\/assets\/b9b5f501-be14-4e3f-9ad8-a87e17ec16e9.png","name":"[AB] Web Pop Up Banner - Blog RG","targetUrl":"https:\/\/bayar.ruangguru.com\/?utm-source=ab-web-pop-up-banner-blog-rg"}],"endDate":null,"hide":0,"imageUrl":"https:\/\/cdn-web-2.ruangguru.com\/\/landing-pages\/assets\/4680961a-4e01-4169-8ff4-da0823d0da6c.png","name":"[RG] Popup Banner Blog - Promo SNBT Ramadan","nc_v5ij___rg_campaign_id":null,"nc_v5ij___rg_product_id":41,"product":"ruangguru","rankPosition":1,"rg_campaign":null,"rg_product":{"Id":41,"name":"ruangguru"},"showIn":"blog","startDate":null,"type":"popup"},{"CreatedAt":"2025-07-25 01:01:27+00:00","Id":705,"UpdatedAt":"2026-02-23 10:52:46+00:00","campaign":null,"cta":[{"Id":33341,"ctaId":"ab-web-pop-up-banner-blog-rg-1","ctaLink":"URI::(https:\/\/cta.ruangguru.com\/ab-web-pop-up-banner-blog-rg-1)","imageUrl":"https:\/\/cdn-web-2.ruangguru.com\/landing-pages\/assets\/f30c4943-4456-4a96-858b-fe065c9073ae.png","name":"[AB] Web Pop Up Banner - Blog RG 1","targetUrl":"https:\/\/bayar.ruangguru.com\/?utm-source=ab-web-pop-up-banner-blog-rg"}],"endDate":null,"hide":0,"imageUrl":"https:\/\/cdn-web-2.ruangguru.com\/landing-pages\/assets\/e0ebb0c9-e368-4524-9241-dbaf73cafccd.png","name":"[RG] Popup Banner Blog - Promo TKA Ramadan","nc_v5ij___rg_campaign_id":null,"nc_v5ij___rg_product_id":41,"product":"ruangguru","rankPosition":2,"rg_campaign":null,"rg_product":{"Id":41,"name":"ruangguru"},"showIn":"blog","startDate":null,"type":"popup"},{"CreatedAt":"2023-08-16 13:35:02+00:00","Id":657,"UpdatedAt":"2026-02-06 03:52:10+00:00","campaign":null,"cta":[{"Id":33189,"ctaId":"rasionalisasi-popup-blog-rg","ctaLink":"URI::(https:\/\/cta.ruangguru.com\/rasionalisasi-popup-blog-rg)","imageUrl":"https:\/\/cdn-web-2.ruangguru.com\/landing-pages\/assets\/0ec15e92-707a-4660-8134-11f1c1e539a8.png","name":"[RG] Pop Up Blog - Rasionalisasi","targetUrl":"https:\/\/www.ruangguru.com\/rasionalisasi"}],"endDate":null,"hide":0,"imageUrl":"https:\/\/cdn-web-2.ruangguru.com\/landing-pages\/assets\/0ec15e92-707a-4660-8134-11f1c1e539a8.png","name":"[RG] Pop Up Blog RG - Rasionalisasi","nc_v5ij___rg_campaign_id":null,"nc_v5ij___rg_product_id":41,"product":"ruangguru","rankPosition":3,"rg_campaign":null,"rg_product":{"Id":41,"name":"ruangguru"},"showIn":"blog","startDate":null,"type":"popup"},{"CreatedAt":"2023-12-07 09:26:39+00:00","Id":677,"UpdatedAt":"2026-02-12 02:22:12+00:00","campaign":null,"cta":[{"Id":33305,"ctaId":"to-snbt-reg-2026-popup-blog-rg","ctaLink":"URI::(https:\/\/cta.ruangguru.com\/to-snbt-reg-2026-popup-blog-rg)","imageUrl":"https:\/\/cdn-web-2.ruangguru.com\/landing-pages\/assets\/b95e02b2-28a4-4c24-a6db-930ecddef2fa.jpg","name":"[IDN] CTA Popup Blog RG - Tryout SNBT Regular 2026","targetUrl":"https:\/\/link.ruangguru.com\/blPk\/TOUTBKREG7"}],"endDate":null,"hide":0,"imageUrl":"https:\/\/cdn-web-2.ruangguru.com\/landing-pages\/assets\/b95e02b2-28a4-4c24-a6db-930ecddef2fa.jpg","name":"[RG] Popup Blog RG - Tryout Regular 2026","nc_v5ij___rg_campaign_id":null,"nc_v5ij___rg_product_id":41,"product":"ruangguru","rankPosition":4,"rg_campaign":null,"rg_product":{"Id":41,"name":"ruangguru"},"showIn":"blog","startDate":null,"type":"popup"},{"CreatedAt":"2026-02-05 10:16:52+00:00","Id":689,"UpdatedAt":"2026-03-05 02:41:12+00:00","campaign":null,"cta":[{"Id":33338,"ctaId":"pop-blog-to-snbt-prem","ctaLink":"URI::(https:\/\/cta.ruangguru.com\/pop-blog-to-snbt-prem)","imageUrl":"https:\/\/cdn-web-2.ruangguru.com\/\/landing-pages\/assets\/1b8558a2-ad51-4144-b30c-01a3231a22da.jpg","name":"[RG] Popup Blog - TO SNBT Prem","targetUrl":"https:\/\/link.ruangguru.com\/blPk\/TOUTBKPREM"}],"endDate":null,"hide":0,"imageUrl":"https:\/\/cdn-web-2.ruangguru.com\/\/landing-pages\/assets\/1b8558a2-ad51-4144-b30c-01a3231a22da.jpg","name":"[RG] Pop blog - TO SNBT Prem","nc_v5ij___rg_campaign_id":null,"nc_v5ij___rg_product_id":41,"product":"ruangguru","rankPosition":5,"rg_campaign":null,"rg_product":{"Id":41,"name":"ruangguru"},"showIn":"blog","startDate":null,"type":"popup"},{"CreatedAt":"2023-12-07 09:26:39+00:00","Id":679,"UpdatedAt":"2026-03-04 03:44:16+00:00","campaign":null,"cta":[{"Id":33304,"ctaId":"to-prem-tka-sd-smp-popup-blog-rg","ctaLink":"URI::(https:\/\/cta.ruangguru.com\/to-prem-tka-sd-smp-popup-blog-rg)","imageUrl":"https:\/\/cdn-web-2.ruangguru.com\/landing-pages\/assets\/1bf472e1-62f4-4aa9-ab8c-4fa72a82dd7b.png","name":"[RG] Pop Up Blog RG - TO Premium TKA SD SMP","targetUrl":"https:\/\/s.id\/TOTKAPREMSDSMP"}],"endDate":null,"hide":0,"imageUrl":"https:\/\/cdn-web-2.ruangguru.com\/\/landing-pages\/assets\/e6888a56-1d95-4d8a-b87a-b19b8a185651.png","name":"[RG] Popup Blog RG - TO TKA Premium SD SMP","nc_v5ij___rg_campaign_id":null,"nc_v5ij___rg_product_id":41,"product":"ruangguru","rankPosition":6,"rg_campaign":null,"rg_product":{"Id":41,"name":"ruangguru"},"showIn":"blog","startDate":null,"type":"popup"},{"CreatedAt":"2025-08-25 04:25:04+00:00","Id":672,"UpdatedAt":"2026-02-06 03:52:17+00:00","campaign":null,"cta":[{"Id":33285,"ctaId":"rgp-popup-blog-rg","ctaLink":"URI::(https:\/\/cta.ruangguru.com\/rgp-popup-blog-rg)","imageUrl":"https:\/\/cdn-web-2.ruangguru.com\/landing-pages\/assets\/851003e6-07b5-40d1-9068-f9b0bcb1625a.png","name":"[RG] Pop Up Blog - RGP","targetUrl":"https:\/\/www.ruangguru.com\/privat"}],"endDate":null,"hide":0,"imageUrl":"https:\/\/cdn-web-2.ruangguru.com\/landing-pages\/assets\/851003e6-07b5-40d1-9068-f9b0bcb1625a.png","name":"[RG] Pop Up Blog - RGP","nc_v5ij___rg_campaign_id":null,"nc_v5ij___rg_product_id":41,"product":"ruangguru","rankPosition":7,"rg_campaign":null,"rg_product":{"Id":41,"name":"ruangguru"},"showIn":"blog","startDate":null,"type":"popup"},{"CreatedAt":"2023-08-16 13:35:02+00:00","Id":379,"UpdatedAt":"2026-03-06 01:54:52+00:00","campaign":null,"cta":[{"Id":31356,"ctaId":"25f78174-4fc2-11ef-9a39-4201ac180089","ctaLink":"URI::(https:\/\/cta.ruangguru.com\/25f78174-4fc2-11ef-9a39-4201ac180089)","imageUrl":"https:\/\/cdn-web-2.ruangguru.com\/landing-pages\/assets\/f60bc49c-c00f-4a5e-80a2-2552fa18ae21.jpg","name":"CTA Blog RG - Kitab UTBK SNBT","targetUrl":"https:\/\/bit.ly\/orderkitabrg"}],"endDate":null,"hide":0,"imageUrl":"https:\/\/cdn-web-2.ruangguru.com\/\/landing-pages\/assets\/cbe7b869-fbe2-4497-8a1e-42344df5b137.jpg","name":"[RG] Pop Up Blog RG - Kitab UTBK SNBT","nc_v5ij___rg_campaign_id":null,"nc_v5ij___rg_product_id":41,"product":"ruangguru","rankPosition":8,"rg_campaign":null,"rg_product":{"Id":41,"name":"ruangguru"},"showIn":"blog","startDate":null,"type":"popup"},{"CreatedAt":"2023-08-16 13:35:02+00:00","Id":587,"UpdatedAt":"2026-03-06 01:55:00+00:00","campaign":null,"cta":[{"Id":33020,"ctaId":"kitab-tka-smp-popup-blog","ctaLink":"URI::(https:\/\/cta.ruangguru.com\/kitab-tka-smp-popup-blog)","imageUrl":"https:\/\/cdn-web-2.ruangguru.com\/landing-pages\/assets\/9ea9eca7-9ef7-433c-baad-14bc1019f890.jpg","name":"[RG] Pop up blog - Kitab TKA SMP","targetUrl":"https:\/\/bit.ly\/kitabtkasmprg"}],"endDate":null,"hide":0,"imageUrl":"https:\/\/cdn-web-2.ruangguru.com\/\/landing-pages\/assets\/eb41ad00-e4dc-46f5-b9f6-721266fc371e.jpg","name":"[RG] Pop Up Blog RG - Kitab TKA SMP","nc_v5ij___rg_campaign_id":null,"nc_v5ij___rg_product_id":41,"product":"ruangguru","rankPosition":9,"rg_campaign":null,"rg_product":{"Id":41,"name":"ruangguru"},"showIn":"blog","startDate":null,"type":"popup"},{"CreatedAt":"2025-11-12 10:28:45+00:00","Id":636,"UpdatedAt":"2026-02-06 03:52:20+00:00","campaign":null,"cta":[{"Id":33149,"ctaId":"pop-rg-kitab-utbk-snbt-lite","ctaLink":"URI::(https:\/\/cta.ruangguru.com\/pop-rg-kitab-utbk-snbt-lite)","imageUrl":"https:\/\/cdn-web-2.ruangguru.com\/landing-pages\/assets\/8d6f8639-cfff-4d64-89ea-f68bfe7a868c.png","name":"[RG] Pop blog - Kitab utbk snbt lite","targetUrl":"https:\/\/s.id\/litesnbt26"}],"endDate":null,"hide":0,"imageUrl":"https:\/\/cdn-web-2.ruangguru.com\/landing-pages\/assets\/f7908ac1-3b0b-492c-bf87-dcea2b20b87c.png","name":"[RG] Pop blog - Kitab utbk snbt lite","nc_v5ij___rg_campaign_id":null,"nc_v5ij___rg_product_id":41,"product":"ruangguru","rankPosition":10,"rg_campaign":null,"rg_product":{"Id":41,"name":"ruangguru"},"showIn":"blog","startDate":null,"type":"popup"},{"CreatedAt":"2025-11-14 08:09:42+00:00","Id":647,"UpdatedAt":"2026-02-06 03:52:21+00:00","campaign":null,"cta":[{"Id":33160,"ctaId":"pop-rg-kitablitetkasmp","ctaLink":"URI::(https:\/\/cta.ruangguru.com\/pop-rg-kitablitetkasmp)","imageUrl":"https:\/\/cdn-web-2.ruangguru.com\/landing-pages\/assets\/20edba9b-ef84-4938-b698-4a82783478a5.png","name":"[RG] Pop blog - kitab lite tka smp","targetUrl":"https:\/\/s.id\/litetkasmp26"}],"endDate":null,"hide":0,"imageUrl":"https:\/\/cdn-web-2.ruangguru.com\/landing-pages\/assets\/50097055-1862-46a8-bbe0-fa5b077f88bb.png","name":"[RG] Pop blog - kitab lite tka smp","nc_v5ij___rg_campaign_id":null,"nc_v5ij___rg_product_id":41,"product":"ruangguru","rankPosition":11,"rg_campaign":null,"rg_product":{"Id":41,"name":"ruangguru"},"showIn":"blog","startDate":null,"type":"popup"}]';
var jsArray = JSON.parse(jsonString);
console.log(jsArray);
</script>
<script>
let windowHeight = window.innerHeight;
let promosLength = 11;
document.addEventListener('DOMContentLoaded', function() {
// Initialize Bootstrap Modal
let popupPromo = new bootstrap.Modal(document.getElementById('popupPromo'), {});
// Initialize Glider.js inside the Bootstrap Modal
function initGliderInModal() {
new Glider(document.querySelector('#popupPromo .glider'), {
slidesToScroll: 1,
slidesToShow: 1,
draggable: true,
dots: '#popup-promo-dots',
arrows: {
prev: '#popup-promo-prev',
next: '#popup-promo-next'
}
});
}
// Show Bootstrap Modal and initialize Glider.js after a specified scroll amount
const scrollThreshold = 2 / 3 * windowHeight; // The scroll amount in pixels to trigger the Modal
let gliderInitialized = false;
window.addEventListener('scroll', function() {
if (window.scrollY >= scrollThreshold && !gliderInitialized && promosLength > 0) {
popupPromo.show();
// Listen for the 'shown' event to initialize Glider.js after the Modal has been fully displayed
$('#popupPromo').on('shown.bs.modal', function() {
initGliderInModal();
gliderInitialized = true;
// Optionally, remove the 'shown' event listener after initializing the Glider to avoid re-initializing
$('#popupPromo').off('shown.bs.modal');
});
// Remove the scroll event listener after the Modal is shown to avoid re-initializing the Glider
this.removeEventListener('scroll', arguments.callee);
}
});
});
</script>
<script src="https://unpkg.com/analytics@0.8.1/dist/analytics.min.js"></script>
<script type="text/javascript" src="https://unpkg.com/analytics-plugin-trackable-min@0.4.5/dist/analytics-plugin-trackable.min.js"></script>
<script type="text/javascript" defer>
/* Initialize analytics */
var Analytics = window._analytics.init({
app: "ruangguruLanding",
debug: false,
plugins: [analyticsTrackable()],
});
/* Additional context tracker pageView */
const post_id = 5041;
const tags_id = [31,10,37];
const category_id = 467;
const sub_category_id = 475;
const customData = {
tags_id: tags_id,
category_id: category_id,
sub_category_id: sub_category_id,
post_id: post_id,
};
Analytics.plugins.trackable.context(JSON.stringify(customData));
Analytics.ready(function () {
Analytics.page();
});
$(document).on('click', '[data-tracking-event-type]', function (event) {
const eventType = $(this).data('tracking-event-type');
const context = $(this).data('tracking-context');
Analytics.track(eventType, context);
});
</script>
<footer class="footer">
<div class="container">
<div class="row">
<div class="col-lg-3">
<div class="office">
<a href="https://www.ruangguru.com/">
<img src="https://cdn-web-2.ruangguru.com/static/RG_LOGO_WHITE.png?convert=auto" alt="Logo Ruangguru" loading="lazy" />
</a>
<address>
<p class="hq">RUANGGURU HQ</p>
<p>
Gedung Sinarmas MSIG Tower Lt. 33. Jl. Jenderal Sudirman Kav. 21, Karet Kuningan, Setiabudi, Jakarta Selatan, Jakarta 12920
</p>
</address>
</div>
<nav class="footer-menu call-us">
<p class="title">Hubungi Kami</p>
<address>
<a href="mailto:info@ruangguru.com">
<img class="icon-call-us" src="https://cdn-web-2.ruangguru.com/file-uploader/lp/4739a139-8f09-42ea-b517-d842c5d1c28d.png" loading="lazy" alt="Logo Email Footer" />
info@ruangguru.com</a>
<a href="tel:02130930000">
<img class="icon-call-us" src="https://cdn-web-2.ruangguru.com/file-uploader/lp/6f4bb6c8-52c9-4acb-859b-47a10a7eec75.png" loading="lazy" alt="Logo Phone Footer" />(021) 3093 0000</a>
<a href="https://wa.me/6281574410000">
<img class="icon-call-us" src="https://cdn-web-2.ruangguru.com/file-uploader/lp/4b58468a-b2f9-40e4-867f-d3242a065dcf.png" loading="lazy" alt="Logo Whatsapp Footer" />0815 7441 0000</a>
</address>
</nav>
<nav class="footer-menu social d-none d-lg-block">
<p class="title">Ikuti Kami</p>
<a target="_blank" href="https://www.instagram.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/instagram.png" loading="lazy" alt="Logo Instagram Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.facebook.com/ruanggurucom/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/facebook.png" loading="lazy" alt="Logo Facebook Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://twitter.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/twitter.png" loading=" lazy" alt="Logo Twitter Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.youtube.com/ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/youtube.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/youtube.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/youtube.png" loading=" lazy" alt="Logo Youtube Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.linkedin.com/company/ruangguru-com">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/linkedin.png" loading=" lazy" alt="Logo LinkedIn Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.tiktok.com/@ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/tiktok.png" loading=" lazy" alt="Logo TikTok Footer" width="32px" height="32px" />
</picture>
</a>
</nav>
</div>
<div class="col-lg-9">
<div class="row">
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title">Produk Ruangguru</p>
<ul type="none">
<li><a href="https://roboguru.ruangguru.com" target="_blank">Roboguru</a></li>
<li><a href="https://www.ruangguru.com/roboguruplus">Roboguru Plus</a></li>
<li><a href="https://www.ruangguru.com/dafa-lulu">Dafa dan Lulu</a></li>
<li><a href="https://www.ruangguru.com/for-kids/kursus">Kursus for Kids</a></li>
<li><a href="https://www.ruangguru.com/for-kids">Ruangguru for Kids</a></li>
<li><a href="https://www.ruangguru.com/bisnis">Ruangguru for Business</a></li>
<li><a href="https://www.ruangguru.com/ruanguji">Ruanguji</a></li>
<li><a href="https://www.ruangguru.com/blog">Ruangbaca</a></li>
<li><a href="https://www.ruangguru.com/ruangkelas">Ruangkelas</a></li>
<li><a href="https://www.ruangguru.com/ruangbelajar">Ruangbelajar</a></li>
<li><a href="https://pengajar.ruangguru.com/">Ruangpengajar</a></li>
<li><a href="https://www.ruangguru.com/privat">Ruangguru Privat</a></li>
<li><a href="https://www.ruangpeduli.org/" target="_blank">Ruangpeduli</a></li>
</ul>
</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title">Bantuan & Panduan</p>
<ul type="none">
<li><a href="https://www.ruangguru.com/company-credentials">Company Credentials</a></li>
<li><a href="https://www.ruangguru.com/beasiswa">Beasiswa Ruangguru</a></li>
<li><a href="https://www.ruangguru.com/cicilan">Cicilan Ruangguru</a></li>
<li><a href="https://www.ruangguru.com/promo">Promo Ruangguru</a></li>
<li><a href="https://ticketing.ruangguru.com/help?request_type_id=459" target="_blank">Vulnerability Report</a></li>
<li><a href="https://www.ruangguru.com/bantuan#layanan">Layanan Pengaduan</a></li>
<li><a href="https://www.ruangguru.com/terms-conditions">Syarat & Ketentuan</a></li>
<li><a href="https://www.ruangguru.com/privacy-policy">Kebijakan Privasi</a></li>
<li><a href="https://www.ruangguru.com/about-us">Tentang Kami</a></li>
<li><a href="https://www.ruangguru.com/contact-us">Kontak Kami</a></li>
<li><a href="https://www.ruangguru.com/press">Press Kit</a></li>
<li><a href="https://www.ruangguru.com/bantuan">Bantuan</a></li>
<li><a href="https://career.ruangguru.com/">Karier</a></li>
</ul>
</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title">Produk Lainnya</p>
<ul type="none">
<li><a href="https://www.brainacademy.id/" target="_blank">Brain Academy</a></li>
<li><a href="https://www.english-academy.id/" target="_blank">English Academy</a></li>
<li><a href="https://skillacademy.com/" target="_blank">Skill Academy</a></li>
<li><a href="https://www.ruangkerja.id/" target="_blank">Ruangkerja</a></li>
<li><a href="https://www.schoters.com/id/" target="_blank">Schoters</a></li>
<li><a href="https://www.kalananti.id/" target="_blank">Kalananti</a></li>
</ul>
</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title"> Coba GRATIS Aplikasi Ruangguru</p>
<div class="download-list">
<ul>
<li>
<a target="_blank" rel="nofollow" href="https://apps.apple.com/id/app/ruangguru-solusi-belajar/id1099742206?l=id">
<img src="https://cdn-web-2.ruangguru.com/static/appstore.png" loading="lazy" alt="Button App Store Footer " />
</a>
</li>
<li>
<a target="_blank" rel="nofollow" href="https://play.google.com/store/apps/details?id=com.ruangguru.livestudents&hl=in">
<img src="https://cdn-web-2.ruangguru.com/static/googleplay.png" loading="lazy" alt="Button Google Play Footer " />
</a>
</li>
<li>
<a target="_blank" rel="nofollow" href="https://appgallery.huawei.com/#/app/C102352375">
<img src="https://cdn-web-2.ruangguru.com/static/huawei.png" loading="lazy" alt="Button AppGallery Footer " />
</a>
</li>
</ul>
</div>
</nav>
</div>
</div>
</div>
</div>
<div class="d-lg-none text-center">
<nav class="footer-menu social">
<p class="title">Ikuti Kami</p>
<a target="_blank" href="https://www.instagram.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/instagram.png" loading="lazy" alt="Logo Instagram Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.facebook.com/ruanggurucom/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/facebook.png" loading="lazy" alt="Logo Facebook Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://twitter.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/twitter.png" loading=" lazy" alt="Logo Twitter Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.youtube.com/ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/youtube.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/youtube.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/youtube.png" loading=" lazy" alt="Logo Youtube Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.linkedin.com/company/ruangguru-com">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/linkedin.png" loading=" lazy" alt="Logo LinkedIn Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.tiktok.com/@ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/tiktok.png" loading=" lazy" alt="Logo TikTok Footer" width="32px" height="32px" />
</picture>
</a>
</nav>
</div>
<p class="footer-copyright">
© 2026 All Rights Reserved PT. Ruang Raya Indonesia
</p>
</div>
<style>
.bantuan-container {
position: relative;
}
.bantuan-element {
position: fixed;
z-index: 999;
display: flex;
align-items: flex-end;
justify-content: flex-end;
cursor: pointer;
transition: all 0.6s ease;
}
.bantuan-top {
bottom: 11rem;
right: 2rem;
}
.bantuan-bottom {
bottom: 2rem;
right: 2rem;
}
.bantuan-top-2 {
bottom: 15rem;
right: 2rem;
}
.bantuan-top-3 {
bottom: 19rem;
right: 2rem;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 2rem;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 2rem;
}
@media (min-width: 768px) {
.bantuan-element img {
width: auto;
transition: all 0.4s ease;
}
.bantuan-top img {
width: 140px;
}
.bantuan-bottom img {
width: 140px;
}
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 140px;
}
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 140px;
}
.bantuan-element.clicked {
bottom: 9rem;
right: 2.5rem;
}
.bantuan-element.clicked img {
width: auto;
height: 64px;
}
}
@media (max-width: 767px) {
.bantuan-top {
bottom: 8rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom {
bottom: 2rem;
right: 1.25rem;
align-items: center;
}
.bantuan-top-2 {
bottom: 12rem;
right: 1rem;
align-items: center;
}
.bantuan-top-3 {
bottom: 16rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 1.25rem;
align-items: center;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 1.25rem;
align-items: center;
}
.bantuan-element img {
width: auto;
}
.bantuan-top img,
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 96px;
}
.bantuan-bottom img,
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 96px;
}
}
.bantuan-element:hover {
transform: scale(1.05);
}
.bantuan-element img {
max-width: 100%;
height: auto;
}
</style>
<div id="bantuan-divs-container" style="position: relative" data-product="ruangguru" data-table="rg_floating_icon"></div>
<script>
class FloatingDivsComponent {
constructor(product = 'ruangguru', table = 'rg_floating_icon') {
this.container = document.getElementById('bantuan-divs-container');
this.floatingElements = [];
this.product = product;
this.table = table;
// Configuration
this.config = {
baseApiUrl: 'https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/rg_banner/views/',
apiKey: 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
maxElements: 2,
zIndexBase: 100,
};
// Build dynamic API URL based on table parameter
this.config.apiUrl = this.buildApiUrl();
this.init();
}
buildApiUrl() {
const baseUrl = this.config.baseApiUrl;
const tableName = this.table || 'rg_floating_icon';
const queryParams =
'offset=0&limit=99999&sort=rankPosition&where=(type,eq,floating)~and(showIn,anyof,blog)~and(hide,is,false)~and(product,eq,' +
this.product +
')&nested%5Bcta%5D%5Bfields%5D=Id,name,ctaId,imageUrl,ctaLink,targetUrl';
return `${baseUrl}${tableName}?${queryParams}`;
}
async init() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to initialize floating divs component:', error);
}
}
async fetchFloatingElements() {
try {
const options = {
method: 'GET',
headers: {
'xc-token': this.config.apiKey || 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
},
};
const urlNoco = this.config.apiUrl;
const response = await fetch(urlNoco, options);
if (!response.ok) {
throw new Error(`HTTP error! status: ${response.status}`);
}
const data = await response.json();
this.floatingElements = this.processApiResponse(data);
} catch (error) {
console.error('Error fetching floating elements:', error);
throw error;
}
}
processApiResponse(data) {
if (!data || !data.list || !Array.isArray(data.list)) {
return [];
}
console.log(data.list);
// Ensure we only get maximum 2 elements
const limitedElements = data.list.slice(0, this.config.maxElements);
return limitedElements;
}
renderFloatingElements() {
if (!this.container || this.floatingElements.length === 0) {
return;
}
// Additional safeguard: ensure we never render more than maxElements
const elementsToRender = this.floatingElements.slice(0, this.config.maxElements);
// Clean up existing elements and their event listeners
this.cleanupExistingElements();
// Clear existing content
this.container.innerHTML = '';
elementsToRender.forEach((element, index) => {
const floatingDiv = this.createFloatingDiv(element, index);
this.container.appendChild(floatingDiv);
});
}
cleanupExistingElements() {
// Clear existing elements (no need for event listener cleanup with CSS approach)
const existingElements = this.container.querySelectorAll('[data-floating-element]');
existingElements.forEach(element => {
element.remove();
});
}
createFloatingDiv(element, index) {
const div = document.createElement('div');
const cta = element.cta[0]; // Use the first CTA
// Add data attribute for cleanup tracking
div.setAttribute('data-floating-element', 'true');
// Apply CSS classes based on rankPosition
const positionClass = this.getPositionClass(element.rankPosition, index);
div.className = `bantuan-element ${positionClass}`;
div.style.zIndex = this.config.zIndexBase + index;
// Create the link and image
const link = document.createElement('a');
link.href = 'https://cta.ruangguru.com/' + cta.ctaId || '#';
link.target = '_blank';
// Add tracking attributes
link.setAttribute('data-tracking-event-type', 'landing_page__core__item_click');
link.setAttribute(
'data-tracking-context',
JSON.stringify({
product_name: this.product,
cta_action: 'redirection',
cta_action_detail: link.href,
item_type: 'floating',
item_name: element.name || 'Floating element',
item_category: 'payment',
item_position: index,
item_serial: null,
section_type: 'floating_item',
section_position: 'body',
section_name: 'floating_item',
})
);
const img = document.createElement('img');
img.src = element.imageUrl + '?h=200&convert=webp';
img.alt = element.name || 'Floating element';
img.loading = 'lazy';
// Add click tracking
link.addEventListener('click', () => {
this.trackClick(element, cta);
});
link.appendChild(img);
div.appendChild(link);
return div;
}
getPositionClass(rankPosition, index) {
// Define positioning classes based on rankPosition
if (rankPosition === 1) {
return 'bantuan-top'; // Top position
} else if (rankPosition === 2) {
return 'bantuan-bottom'; // Bottom position
} else {
// For additional elements, distribute them evenly
return `bantuan-${index % 2 === 0 ? 'top' : 'bottom'}-${Math.floor(index / 2) + 1}`;
}
}
trackClick(element, cta) {
// Implement click tracking logic here
console.log('Floating element clicked:', {
elementId: element.Id,
elementName: cta.name,
ctaId: cta.ctaId,
targetUrl: cta.targetUrl,
});
}
// Public method to manually refresh
async refresh() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to refresh floating elements:', error);
throw error;
}
}
// Public method to get current floating elements
getFloatingElements() {
return [...this.floatingElements];
}
}
// Initialize the component when DOM is ready
document.addEventListener('DOMContentLoaded', () => {
// Get product and table parameters from data attributes
const container = document.getElementById('bantuan-divs-container');
const product = container.getAttribute('data-product') || 'ruangguru';
const table = container.getAttribute('data-table') || 'rg_floating_icon';
new FloatingDivsComponent(product, table);
});
// Export for use in other modules if needed
if (typeof module !== 'undefined' && module.exports) {
module.exports = FloatingDivsComponent;
}
</script> <div id="wp-install-nudge" style="
position: fixed;
bottom: 0rem;
right: 0;
z-index: 999;
cursor: pointer;
"></div>
<script>
(function (w, d, s, o, f, js, fjs) {
w['Sales-Nudge-Widget'] = o; w[o] = w[o] || function () { (w[o].q = w[o].q || []).push(arguments) };
js = d.createElement(s), fjs = d.getElementsByTagName(s)[0];
js.id = o; js.src = f; js.async = 1; fjs.parentNode.insertBefore(js, fjs);
}(window, document, 'script', 'wpInstallNudge', 'https://cdn-web-2.ruangguru.com/sales-nudge/6198a95130/dist/widget.js'));
wpInstallNudge('init', { targetElementId: 'wp-install-nudge', clientTarget: 'ruangguru_blog' });
</script>
<script>
// note: disabled due to auto reload page
// var lastScrollTop = 0;
// $(window).scroll(function(event){
// var st = $(this).scrollTop();
// if (st > lastScrollTop){
// $('#wp-install-nudge').slideDown( "slow", function() {});
// } else {
// $('#wp-install-nudge').slideUp( "slow", function() {});
// }
// lastScrollTop = st;
// });
// $(document).ready(function () {
// $("#wp-install-nudge").hide();
// });
$('#wp-install-nudge').click(function(){
Analytics.track("promotion__install_nudge__click",
{
user_email: "ruangguru@blog.com",
cta_link: widgetData.dataConfig.target_link
}).catch((err) => {
console.log("tracker error", err);
});
});
</script>
</footer>
<div id="__next"></div>
<script type="speculationrules">
{"prefetch":[{"source":"document","where":{"and":[{"href_matches":"\/blog\/*"},{"not":{"href_matches":["\/blog\/wp-*.php","\/blog\/wp-admin\/*","\/blog\/wp-content\/uploads\/*","\/blog\/wp-content\/*","\/blog\/wp-content\/plugins\/*","\/blog\/wp-content\/themes\/ruangguru\/*","\/blog\/*\\?(.+)"]}},{"not":{"selector_matches":"a[rel~=\"nofollow\"]"}},{"not":{"selector_matches":".no-prefetch, .no-prefetch a"}}]},"eagerness":"conservative"}]}
</script>
<script>
async function getCtaDetails(ctaIds) {
const endpoint =
" https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/CTA/views/CTA?offset=0&limit=10&where=(ctaId,in," + ctaIds.toString() + ")";
try {
const response = await fetch(endpoint, {
headers: {
"xc-token": "-hG2nBDJzSj0agSgNtcJx97M4F02y54nUMoY6plJ",
},
});
const data = await response.json();
const ctaList = data?.list || [];
const ctaMap = new Map();
for (const ctaData of ctaList) {
ctaMap.set(ctaData.ctaId, ctaData);
}
return ctaMap;
} catch (error) {
console.error("Error fetching CTA details:", error);
return new Map();
}
}
async function replaceCTA() {
const regex = /{{cta\((‘(.*?)’|“(.*?)”)\)}}/g;
const bodyHTML = document.body.innerHTML;
const matches = Array.from(bodyHTML.matchAll(regex));
const ctaIds = matches.map((match) => {
let ctaId = match[2] ?? match[3];
return ctaId;
});
const ctaMap = await getCtaDetails(ctaIds);
const replacedHTML = bodyHTML.replace(regex, (match, _inner, ctaId1, ctaId2) => {
const ctaId = ctaId1 ?? ctaId2;
const ctaData = ctaMap.get(ctaId);
if (ctaData) {
return `<a href="https://cta.ruangguru.com/${ctaData.ctaId}" target="_${ctaData.targetType}" style="position:relative;display:inline-block;">
<img src="${ctaData.imageUrl}" loading="lazy" alt="${ctaData.altText}" />
</a>`;
} else {
return match;
}
});
document.body.innerHTML = replacedHTML;
}
</script>
<meta name="author" content="Ruangguru Tech Team">
<!-- Google Tag Manager (noscript) -->
<noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-PVNLZFT" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript>
<!-- Tracker -->
<script type="text/javascript" src="https://cdn-web-2.ruangguru.com/landing-page-web/public/staticpages/global-assets/js/cta.js"></script>
<script src="https://unpkg.com/@dotlottie/player-component@latest/dist/dotlottie-player.mjs" type="module"></script>
</body>
</html>