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  "body": "\n## Statement\n\nLet $R$ be a ring and let $m, n, p, q \\ge 0$ be integers.\nLet $A$ be an $m \\times n$ matrix, $B$ an $n \\times p$ matrix and $C$ a $p \\times q$ matrix over $R$.\nThen $(AB)C = A(BC)$, where the products are [[matrix products|032Q9FB8MT]].\n\n## Remarks\n\nBoth sides have entry $(i, l)$ equal to $\\sum_{j=1}^{n} \\sum_{k=1}^{p} a_{ij} b_{jk} c_{kl}$.\nBecause of this property, the product $ABC$ needs no parentheses.\nThe property also follows from the associativity of the composition of linear maps.\n\n## Explanations\n\n### L1 human\n\nWhen we multiply three matrices, we may multiply the first two first, or the last two first.\nThe result is the same in both cases.\nThis is like $(2 \\cdot 3) \\cdot 4 = 2 \\cdot (3 \\cdot 4)$ for numbers.\n",
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