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  "body": "\n## Definition\n\nLet $S$ be a set and let $\\ast$ be a [[binary operation|0M418FE7BB]] on $S$.\nThe operation $\\ast$ is commutative when $a \\ast b = b \\ast a$ for all $a, b \\in S$.\n\n## Remarks\n\nAddition and multiplication of real numbers are commutative.\nSubtraction is not commutative: $1 - 2 \\neq 2 - 1$.\nMultiplication of $2 \\times 2$ real matrices is associative but not commutative.\n\n## Explanations\n\n### L1 human\n\nCommutativity says that the order of the two inputs does not matter.\nFor example, $3 \\times 5$ and $5 \\times 3$ are both $15$.\nMany operations do not have this property, for example subtraction and the composition of rotations in space.\n",
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