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  "body": "\n## Description\n\nLet $R$ be a ring and let $n \\ge 0$ be an integer.\nThe *identity matrix* $I_n$ is the $n \\times n$ [[matrix|0VD9ZSWWJG]] over $R$ with entries $1$ on the main diagonal and $0$ elsewhere.\nIts entries are $(I_n)_{ij} = \\delta_{ij}$, where $\\delta_{ij} = 1$ if $i = j$ and $\\delta_{ij} = 0$ otherwise.\nFor each $m \\times n$ matrix $A$, $A I_n = A$ and $I_m A = A$.\n\n## Remarks\n\nThe identity matrix $I_n$ is the identity element of the [[matrix ring|0FHVPRAE60]] $M_n(R)$.\nIt is the matrix of the identity map in any basis.\nFor example, $I_2 = \\begin{pmatrix} 1 \u0026 0 \\\\ 0 \u0026 1 \\end{pmatrix}$.\n\n## Explanations\n\n### L1 human\n\nThe identity matrix has ones on the diagonal and zeros everywhere else.\nIt plays the role of the number $1$: multiplying by it changes nothing.\nAs a map, it leaves each vector where it is.\n",
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        "what": "section Invariants",
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