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  "body": "\n## Example\n\nLet $n$ be a positive integer and let $\\mathrm{GL}_n(\\mathbb{R})$ be the group of invertible $n \\times n$ real matrices under multiplication.\nThe determinant is a map $\\det \\colon \\mathrm{GL}_n(\\mathbb{R}) \\to \\mathbb{R}^\\times$ to the group of nonzero real numbers under multiplication.\nIt is a [[group homomorphism|0JYTG5K9Y4]], because $\\det(AB) = \\det(A) \\det(B)$ for all $A, B$.\n\n## Remarks\n\nThe [[kernel|0W88CEGQP1]] of $\\det$ is the special linear group $\\mathrm{SL}_n(\\mathbb{R})$ of matrices of determinant $1$, so this group is normal in $\\mathrm{GL}_n(\\mathbb{R})$.\nThe determinant is surjective onto $\\mathbb{R}^\\times$, so $\\mathrm{GL}_n(\\mathbb{R}) / \\mathrm{SL}_n(\\mathbb{R}) \\cong \\mathbb{R}^\\times$.\nThe same holds over each field $F$, with $\\mathrm{GL}_n(F)$, $\\mathrm{SL}_n(F)$ and $F^\\times$.\n\n## Explanations\n\n### L1 human\n\nThe determinant turns a product of matrices into a product of numbers.\nThat is exactly what a homomorphism does.\nThe matrices that it sends to $1$ form an important subgroup, the special linear group.\n",
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