{"id":64891,"date":"2025-06-20T10:11:43","date_gmt":"2025-06-20T07:11:43","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=64891"},"modified":"2025-06-20T10:11:43","modified_gmt":"2025-06-20T07:11:43","slug":"determinant-multiplication","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/mathematics\/determinant-multiplication\/","title":{"rendered":"Determinant 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\">Determinant Product Solver<\/h2><\/div><div class=\"relative group inline-block\">\n  <button class=\"favorite\" id=\"favorite\" data-favorite-id=\"64891\" data-favorite-title=\"Determinant Multiplication\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/mathematics\/determinant-multiplication\/\" data-favorite-excerpt=\"This calculator helps you compute the product of determinants of two square matrices. It is ideal for students and professionals working with linear algebra, simplifying determinant multiplication for square matrices of any size.\" 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\/determinant-multiplication\/\" method=\"POST\" class=\"calculator\" id=\"calculator-64891\" data-post=\"64891\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field is-single\" id=\"input-1\"><label for=\"field-1\">Matrix Size<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"matrix_size\"><option value=\"2\">2 \u00d7 2<\/option><option value=\"3\">3 \u00d7 3<\/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-2\"><span class=\"font-semibold\">Matrix A<\/span><\/div><div class=\"field\" id=\"input-3\"><label for=\"field-3\">a\u2081\u2081<\/label><input type=\"number\" name=\"a\" id=\"field-3\" step=\"any\" value=\"1\"\/><\/div><div class=\"field\" id=\"input-4\"><label for=\"field-4\">a\u2081\u2082<\/label><input type=\"number\" name=\"a\" id=\"field-4\" step=\"any\" value=\"2\"\/><\/div><div class=\"field\" id=\"input-5\" hidden><label for=\"field-5\">a\u2081\u2083<\/label><input type=\"number\" name=\"a\" id=\"field-5\" step=\"any\" value=\"3\"\/><\/div><div class=\"field\" id=\"input-6\"><label for=\"field-6\">a\u2082\u2081<\/label><input type=\"number\" name=\"a\" id=\"field-6\" step=\"any\" value=\"4\"\/><\/div><div class=\"field\" id=\"input-7\"><label for=\"field-7\">a\u2082\u2082<\/label><input type=\"number\" name=\"a\" id=\"field-7\" step=\"any\" value=\"5\"\/><\/div><div class=\"field\" id=\"input-8\" hidden><label for=\"field-8\">a\u2082\u2083<\/label><input type=\"number\" name=\"a\" id=\"field-8\" step=\"any\" value=\"6\"\/><\/div><div class=\"field\" id=\"input-9\" hidden><label for=\"field-9\">a\u2083\u2081<\/label><input type=\"number\" name=\"a\" id=\"field-9\" step=\"any\" value=\"7\"\/><\/div><div class=\"field\" id=\"input-10\" hidden><label for=\"field-10\">a\u2083\u2082<\/label><input type=\"number\" name=\"a\" id=\"field-10\" step=\"any\" value=\"8\"\/><\/div><div class=\"field\" id=\"input-11\" hidden><label for=\"field-11\">a\u2083\u2083<\/label><input type=\"number\" name=\"a\" id=\"field-11\" step=\"any\" value=\"9\"\/><\/div><div class=\"is-single field\" id=\"input-12\"><span class=\"font-semibold\">Matrix B<\/span><\/div><div class=\"field\" id=\"input-13\"><label for=\"field-13\">b\u2081\u2081<\/label><input type=\"number\" name=\"b\" id=\"field-13\" step=\"any\" value=\"1\"\/><\/div><div class=\"field\" id=\"input-14\"><label for=\"field-14\">b\u2081\u2082<\/label><input type=\"number\" name=\"b\" id=\"field-14\" step=\"any\" value=\"0\"\/><\/div><div class=\"field\" id=\"input-15\" hidden><label for=\"field-15\">b\u2081\u2083<\/label><input type=\"number\" name=\"b\" id=\"field-15\" step=\"any\" value=\"0\"\/><\/div><div class=\"field\" id=\"input-16\"><label for=\"field-16\">b\u2082\u2081<\/label><input type=\"number\" name=\"b\" id=\"field-16\" step=\"any\" value=\"0\"\/><\/div><div class=\"field\" id=\"input-17\"><label for=\"field-17\">b\u2082\u2082<\/label><input type=\"number\" name=\"b\" id=\"field-17\" step=\"any\" value=\"1\"\/><\/div><div class=\"field\" id=\"input-18\" hidden><label for=\"field-18\">b\u2082\u2083<\/label><input type=\"number\" name=\"b\" id=\"field-18\" step=\"any\" value=\"0\"\/><\/div><div class=\"field\" id=\"input-19\" hidden><label for=\"field-19\">b\u2083\u2081<\/label><input type=\"number\" name=\"b\" id=\"field-19\" step=\"any\" value=\"0\"\/><\/div><div class=\"field\" id=\"input-20\" hidden><label for=\"field-20\">b\u2083\u2082<\/label><input type=\"number\" name=\"b\" id=\"field-20\" step=\"any\" value=\"0\"\/><\/div><div class=\"field\" id=\"input-21\" hidden><label for=\"field-21\">b\u2083\u2083<\/label><input type=\"number\" name=\"b\" id=\"field-21\" step=\"any\" value=\"1\"\/><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"64891\">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\" id=\"output-1\"><span class=\"field-title\"><span>|A|<\/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 class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>|B|<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button class=\"copy-result\" data-tooltip=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-3\"><span class=\"field-title\"><span>|A| \u00d7 |B|<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/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=\"64891\" 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 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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>Determinant 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$$\\det(C) = \\det(A) \\times \\det(B)\n$$\n<\/div>\r\n\t<\/figure>\r\n\t<br \/>\n<strong>Where:<\/strong><\/p>\n<ul>\n<li>$$A$$ and $$B$$ are square matrices of the same size<\/li>\n<li>$$\\det(A)$$ is the determinant of matrix $$A$$<\/li>\n<li>$$\\det(B)$$ is the determinant of matrix $$B$$<\/li>\n<li>$$\\det(C)$$ is the product of their determinants<\/li>\n<\/ul>\n<p>\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>Determinant Multiplication \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<p>\n$$A = \\begin{bmatrix} 2 &#038; 3 \\\\ 1 &#038; 4 \\end{bmatrix}, \\quad B =  \\begin{bmatrix} 0 &#038; 5 \\\\ 6 &#038; 7 \\end{bmatrix}$$<\/p>\n<p>$$\\det(A) = (2 \\cdot 4) &#8211; (3 \\cdot 1) = 8 &#8211; 3 = 5 $$<\/p>\n<p>$$\\det(B) = (0 \\cdot 7) &#8211; (5 \\cdot 6) = 0 &#8211; 30 = -30$$<\/p>\n<p>$$\\det(C) = \\det(A) \\times \\det(B) = 5 \\times (-30) = -150$$<\/p>\n\r\n<\/section>\n<p>The product of determinants corresponds to the determinant of the product matrix:<br \/>\n$$\\det(A \\times B) = \\det(A) \\times \\det(B)$$<\/p>\n<p>This property is important in linear algebra and matrix theory, particularly in simplifying matrix product operations. Our calculator ensures accurate and fast determinant multiplication.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This calculator helps you compute the product of determinants of two square matrices. It is ideal for students and professionals working with linear algebra, simplifying determinant multiplication for square matrices of any size.<\/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-64891","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\/64891","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=64891"}],"version-history":[{"count":2,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64891\/revisions"}],"predecessor-version":[{"id":64893,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64891\/revisions\/64893"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=64891"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=64891"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=64891"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}