Commutative operation
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8/28/2026, 4:35:27 PM · Catalpa
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8/28/2026, 4:35:24 PM · Catalpa
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Let $A$ and $B$ be two sets and $*\colon A\times A\longrightarrow B$ be an operation.2
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Then $*$ is said to be commutative if, for all $x,y\in A$, the identity $x*y=y*x$ holds.4
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**Examples:**6
$\bullet$ The addition (so $*=+$) defined on the sets of integers (so $A=B=\Z$) is commutative. As well as any addition defined on a ring.6
$\bullet$ The addition (so $*=+$) defined on the sets of integers (so $A=B=\Z$) is commutative. Thus, for instance, we have $2+5=7=5+2$. As well as any addition defined on a ring.7
$\bullet$ The product of two squared matrices is not commutative.Revision 831
8/2/2026, 7:43:24 AM · Ancient Tree
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8/1/2026, 5:18:21 PM · Sequoia
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Let $A$ and $B$ be two sets and $*\colon A\times A\longrightarrow B$ be an operation. Then $*$ is said to be commutative if, for all $x,y\in A$, the identity $x*y=y*x$ holds. **Examples:** $\bullet$ The addition (so $*=+$) defined on the sets of integers (so $A=B=\Z$) is commutative. As well as any addition defined on a ring. $\bullet$ The product of two squared matrices is not commutative.