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  "body": "\n## Description\n\nLet $R$ be a ring and let $n \\ge 1$ be an integer.\nThe *matrix ring* $M_n(R)$ is the set of $n \\times n$ [[matrices|0VD9ZSWWJG]] over $R$, with [[matrix addition|0Y7H3SAVA1]] and [[matrix multiplication|032Q9FB8MT]].\nIt is a ring, with the [[zero matrix|0ZTKJJDGR7]] as zero and the [[identity matrix|06DW9BAWB1]] $I_n$ as unit.\nIf $R$ is commutative, then $M_n(R)$ is also an algebra over $R$, with [[scalar multiplication|09V6DDACXR]].\n\n## Remarks\n\nFor $n \\ge 2$ and $R \\ne 0$, the ring $M_n(R)$ is not commutative and has nonzero elements whose product is zero.\nThe units of $M_n(R)$ are the [[invertible matrices|0EB9N0S33C]], and they form the [[general linear group|0FCHE902D7]].\nFor a field $F$, the ring $M_n(F)$ is isomorphic to the ring of endomorphisms of $F^n$.\n\n## Explanations\n\n### L1 human\n\nSquare matrices of one fixed size can be added and multiplied, and the result is again a square matrix of that size.\nThey follow most of the rules of numbers.\nThe main differences are that $AB$ can differ from $BA$, and that $AB$ can be zero when $A$ and $B$ are not.\n",
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