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  "body": "\n## Statement\n\nLet $K$ be a commutative ring and let $n \\ge 1$.\nThen $\\det I_n = 1$, where $I_n$ is the [[identity matrix|06DW9BAWB1]] and $\\det$ is the [[determinant|00KDZRW4C0]].\n\n## Remarks\n\nThis is property 3 of the definition of the determinant.\nIt fixes the scale: the unit cube has volume $1$.\nMore generally, the determinant of a diagonal matrix is the product of its diagonal entries.\n\n## Explanations\n\n### L1 human\n\nThe identity matrix leaves every vector where it is.\nIt does not change any volume.\nSo its determinant is $1$.\n",
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