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Commuting in algebra is often used for matrices. Say you have two matrices, A and B. These two matrices are commutative if A * B = B * A.
This rule can also be used in regular binary operations(addition and multiplication). For example, if you have an X and Y. These two numbers would be commutative if X + Y = Y + X. The case is the same for X * Y = Y * X.
There are operations like subtraction and division that are not commutative. These are referred to as noncommutative operations.
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