commutative law

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commutative law, in mathematics, law holding that for a given binary operation (combining two quantities) the order of the quantities is arbitrary; e.g., in addition, the numbers 2 and 5 can be combined as 2+5=7 or as 5+2=7. More generally, in addition, for any two numbers a and b the commutative law is expressed as a+b=b+a. Multiplication of numbers is also commutative, i.e., a×b=b×a. In general, any binary operation, symbolized by ∘, joining mathematical entities A and B obeys the commutative law if AB=BA for all possible choices of A and B. Not all operations are commutative; e.g., subtraction is not since 2-5≠5-2, and division is not since 2/5≠5/2.

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commutative law Rule of combination in mathematics; it requires that an operation on two terms is independent of the order of the terms. Addition and multiplication of numbers is commutative, since a + b = b + a and ab = ba. Vector cross-multiplication does not obey the commutative law.

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commutative law See commutative operation.