# commutative law

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 *A* ∘ *B* = *B* ∘ *A* 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.

*The Columbia Electronic Encyclopedia,* 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.

#### More on *commutative law* from Infoplease:

#### See more Encyclopedia articles on: Mathematics