{"id":64867,"date":"2025-06-20T09:36:08","date_gmt":"2025-06-20T06:36:08","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=64867"},"modified":"2025-06-20T09:45:33","modified_gmt":"2025-06-20T06:45:33","slug":"matrix-multiplication","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/mathematics\/matrix-multiplication\/","title":{"rendered":"Matrix Multiplication Calculator"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 class=\"text-lg font-display font-bold\">Matrix Multiplication Solver<\/h2><\/div><div class=\"relative group inline-block\">\n  <button class=\"favorite\" id=\"favorite\" data-favorite-id=\"64867\" data-favorite-title=\"Matrix Multiplication\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/mathematics\/matrix-multiplication\/\" data-favorite-excerpt=\"This calculator helps you multiply two matrices of compatible dimensions step-by-step. It is perfect for students, engineers, and professionals working with linear algebra, simplifying manual calculations and minimizing errors.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-binary\">\n    <span class=\"icon icon-shape-star-empty\"><\/span>\n  <\/button>\n  <div class=\"absolute right-full -translate-y-1\/2 top-1\/2 mr-2 w-max max-w-xs px-3 py-2 bg-gray-800 text-white text-xs rounded shadow-lg opacity-0 group-hover:opacity-100 transition-opacity duration-200 z-10 pointer-events-none\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/en\/mathematics\/matrix-multiplication\/\" method=\"POST\" class=\"calculator\" id=\"calculator-64867\" data-post=\"64867\"><fieldset class=\"fieldset-input is-3\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field is-single\" id=\"input-1\"><label for=\"field-1\">Matrix A size<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"matrix_a_size\"><option value=\"3x3\">3 \u00d7 3<\/option><option value=\"3x2\">3 \u00d7 2<\/option><option value=\"2x3\">2 \u00d7 3<\/option><option value=\"3x1\">3 \u00d7 1<\/option><option value=\"1x3\">1 \u00d7 3<\/option><option value=\"2x2\">2 \u00d7 2<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><div class=\"field is-single\" id=\"input-2\"><label for=\"field-2\">Matrix B size<\/label><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"matrix_b_size\"><option value=\"3x3\">3 \u00d7 3<\/option><option value=\"3x2\">3 \u00d7 2<\/option><option value=\"2x3\">2 \u00d7 3<\/option><option value=\"3x1\">3 \u00d7 1<\/option><option value=\"1x3\">1 \u00d7 3<\/option><option value=\"2x2\">2 \u00d7 2<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><div class=\"is-single field\" id=\"input-3\"><span class=\"font-semibold\">Matrix A<\/span><\/div><div class=\"field\" id=\"input-4\"><label for=\"field-4\">A11<\/label><input type=\"number\" name=\"a11\" id=\"field-4\" step=\"any\" value=\"1\"\/><\/div><div class=\"field\" id=\"input-5\"><label for=\"field-5\">A12<\/label><input type=\"number\" name=\"a12\" id=\"field-5\" step=\"any\" value=\"2\"\/><\/div><div class=\"field\" id=\"input-6\"><label for=\"field-6\">A13<\/label><input type=\"number\" name=\"a13\" id=\"field-6\" step=\"any\" value=\"3\"\/><\/div><div class=\"field\" id=\"input-7\"><label for=\"field-7\">A21<\/label><input type=\"number\" name=\"a21\" id=\"field-7\" step=\"any\" value=\"4\"\/><\/div><div class=\"field\" id=\"input-8\"><label for=\"field-8\">A22<\/label><input type=\"number\" name=\"a22\" id=\"field-8\" step=\"any\" value=\"5\"\/><\/div><div class=\"field\" id=\"input-9\"><label for=\"field-9\">A23<\/label><input type=\"number\" name=\"a23\" id=\"field-9\" step=\"any\" value=\"6\"\/><\/div><div class=\"field\" id=\"input-10\"><label for=\"field-10\">A31<\/label><input type=\"number\" name=\"a31\" id=\"field-10\" step=\"any\" value=\"7\"\/><\/div><div class=\"field\" id=\"input-11\"><label for=\"field-11\">A32<\/label><input type=\"number\" name=\"a32\" id=\"field-11\" step=\"any\" value=\"8\"\/><\/div><div class=\"field\" id=\"input-12\"><label for=\"field-12\">A33<\/label><input type=\"number\" name=\"a33\" id=\"field-12\" step=\"any\" value=\"9\"\/><\/div><div class=\"is-single field\" id=\"input-13\"><span class=\"font-semibold\">Matrix B<\/span><\/div><div class=\"field\" id=\"input-14\"><label for=\"field-14\">B11<\/label><input type=\"number\" name=\"b11\" id=\"field-14\" step=\"any\" value=\"9\"\/><\/div><div class=\"field\" id=\"input-15\"><label for=\"field-15\">B12<\/label><input type=\"number\" name=\"b12\" id=\"field-15\" step=\"any\" value=\"8\"\/><\/div><div class=\"field\" id=\"input-16\"><label for=\"field-16\">B13<\/label><input type=\"number\" name=\"b13\" id=\"field-16\" step=\"any\" value=\"7\"\/><\/div><div class=\"field\" id=\"input-17\"><label for=\"field-17\">B21<\/label><input type=\"number\" name=\"b21\" id=\"field-17\" step=\"any\" value=\"6\"\/><\/div><div class=\"field\" id=\"input-18\"><label for=\"field-18\">B22<\/label><input type=\"number\" name=\"b22\" id=\"field-18\" step=\"any\" value=\"5\"\/><\/div><div class=\"field\" id=\"input-19\"><label for=\"field-19\">B23<\/label><input type=\"number\" name=\"b23\" id=\"field-19\" step=\"any\" value=\"4\"\/><\/div><div class=\"field\" id=\"input-20\"><label for=\"field-20\">B31<\/label><input type=\"number\" name=\"b31\" id=\"field-20\" step=\"any\" value=\"3\"\/><\/div><div class=\"field\" id=\"input-21\"><label for=\"field-21\">B32<\/label><input type=\"number\" name=\"b32\" id=\"field-21\" step=\"any\" value=\"2\"\/><\/div><div class=\"field\" id=\"input-22\"><label for=\"field-22\">B33<\/label><input type=\"number\" name=\"b33\" id=\"field-22\" step=\"any\" value=\"1\"\/><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"64867\">Calculate<\/button><button type=\"reset\">Reset<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculate automatically<\/label><small>If enabled, the result will update automatically when you change any value.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Your Results<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>Matrix multiplication result (A \u00d7 B)<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button class=\"copy-result\" data-tooltip=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\"><\/span><\/button><\/div><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Leave a Comment<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"64867\" aria-live=\"polite\"><h2 class=\"text-sm text-gray-500 text-center mb-2\">How did this result make you feel?<\/h2><div class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Like <\/span><\/button><button class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Helpful <\/span><\/button><button class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confused <\/span><\/button><button class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Disappointed <\/span><\/button><button class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\">\u274c <\/span><span class=\"reaction-description font-medium\">Inaccurate <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><ins class=\"adsbygoogle\"\n     style=\"display:block; text-align:center; margin: 32px 0;\"\n     data-ad-layout=\"in-article\"\n     data-ad-format=\"fluid\"\n     data-ad-client=\"ca-pub-1721569815777345\"\n     data-ad-slot=\"6317458308\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n<section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Matrix Multiplication Formula<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n$$C_{ij} = \\sum_{k=1}^{n} A_{ik} B_{kj}$$\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>$$C_{ij}$$ is the element in row i, column j of the product matrix<\/li>\n<li>$$A_{ik}$$ is the element in row i, column k of matrix A<\/li>\n<li>$$B_{kj}$$ is the element in row k, column j of matrix B<\/li>\n<li>$$n$$ is the shared dimension<\/li>\n<\/ul>\n<p>This formula computes each element of the resulting matrix by summing the products of corresponding elements from the rows of matrix A and columns of matrix B.<br \/>\r\n<\/section>\n<section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Matrix Multiplication \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p>$$A = \\begin{bmatrix} 1 &#038; 2 \\\\ 3 &#038; 4 \\end{bmatrix}$$<\/p>\n<p>$$B = \\begin{bmatrix} 5 &#038; 6 \\\\ 7 &#038; 8 \\end{bmatrix}$$<\/p>\n<p>$$C = A \\times B = \\begin{bmatrix} (1 \\cdot 5 + 2 \\cdot 7) &#038; (1 \\cdot 6 + 2 \\cdot 8) \\\\ (3 \\cdot 5 + 4 \\cdot 7) &#038; (3 \\cdot 6 + 4 \\cdot 8) \\end{bmatrix} = \\begin{bmatrix} 19 &#038; 22 \\\\ 43 &#038; 50 \\end{bmatrix}$$<\/p>\n<p>\n\r\n<\/section>\n<p>Matrix multiplication is widely used in linear algebra, computer graphics, machine learning, and physics. The operation combines two matrices where the number of columns in the first equals the number of rows in the second. Our calculator ensures accuracy and saves time when working with large matrices.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This calculator helps you multiply two matrices of compatible dimensions step-by-step. It is perfect for students, engineers, and professionals working with linear algebra, simplifying manual calculations and minimizing errors.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[7],"tags":[69],"class_list":["post-64867","post","type-post","status-publish","format-standard","hentry","category-mathematics","tag-matrix"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64867","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=64867"}],"version-history":[{"count":13,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64867\/revisions"}],"predecessor-version":[{"id":64884,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64867\/revisions\/64884"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=64867"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=64867"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=64867"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}