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  "body": "\n## Example\n\nLet $n \\ge 1$. The [[determinant|0C3CFHDN6R]] is a homomorphism $\\det : \\mathrm{GL}_n(\\mathbb{R}) \\to \\mathbb{R}^\\times$, because $\\det(AB) = \\det(A)\\det(B)$.\nHere $\\mathrm{GL}_n(\\mathbb{R})$ is the [[general linear group|0FCHE902D7]], and $\\mathbb{R}^\\times$ is the group of nonzero real numbers under multiplication.\nThe [[kernel|0Z424HK8CQ]] of $\\det$ is the set of matrices with determinant $1$. This is the [[special linear group|0V9PMN0RBH]] $\\mathrm{SL}_n(\\mathbb{R})$.\nThus $\\mathrm{SL}_n(\\mathbb{R})$ is a [[normal subgroup|0C9ZKYSPYR]] of $\\mathrm{GL}_n(\\mathbb{R})$.\n\n## Remarks\n\nFor $n \\ge 2$, the group $\\mathrm{GL}_n(\\mathbb{R})$ is not abelian. Thus the normality does not come from commutativity.\n",
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