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  "body": "\n## Description\n\nLet $R$ be a ring and let $m, n \\ge 0$ be integers.\nThe $m \\times n$ *zero matrix* over $R$ is the [[matrix|0VD9ZSWWJG]] $0_{m \\times n}$ whose entries are all $0$.\nIt is the identity element for [[matrix addition|0Y7H3SAVA1]]: $A + 0 = 0 + A = A$ for each $m \\times n$ matrix $A$.\nFor each matrix $B$ with $n$ rows, the product $0_{m \\times n} B$ is a zero matrix.\n\n## Remarks\n\nThe $2 \\times 2$ zero matrix is $\\begin{pmatrix} 0 \u0026 0 \\\\ 0 \u0026 0 \\end{pmatrix}$.\nThe zero matrix is the matrix of the zero linear map in any pair of bases.\nA product of two nonzero matrices can be a zero matrix, for example $\\begin{pmatrix} 0 \u0026 1 \\\\ 0 \u0026 0 \\end{pmatrix}^2 = 0$.\n\n## Explanations\n\n### L1 human\n\nThe zero matrix is the table with $0$ in every position.\nIt plays the role of the number $0$: adding it to a matrix changes nothing.\nThere is one zero matrix for each size.\n",
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