**Commutative Operation**

Any operation ⊕ for which *a*⊕*b* = *b*⊕*a**a* and *b*. Addition and multiplication are both commutative. Subtraction, division, and composition of functions are not. For example,

**More**: Commutativity isn't just a property of an operation alone. It's actually a property of an operation over a particular set. For example, when we say addition is commutative over the set of real numbers, we mean that *a + b = b + a**a* and *b*. Subtraction is not commutative over real numbers since we can't say that *a* – *b = b* – *a**a* and *b*. Even though *a* – *b = b* – *a**a* and *b* are the same, that still doesn't make subtraction commutative over the set of all real numbers.

**Further examples**: In this more formal sense, it is correct to say that matrix multiplication is not commutative for square matrices. Even though

**See also**

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