## commutative

com·mu·ta·tive- of commutation; involving exchange or replacement
- Math. of or pertaining to an operation in which the order of the elements does not affect the result, as, in addition, 3 + 2 = 2 + 3 and, in multiplication, 2 × 3 = 3 × 2

## commutative

adjective

- Relating to, involving, or characterized by substitution, interchange, or exchange.
- Independent of order. Used of a logical or mathematical operation that combines objects or sets of objects two at a time. If
*a*×*b*=*b*×*a*, the operation indicated by × is commutative.

*Related Forms:*

**com·mu′ta·tiv′i·ty**noun

## commutative

Adjective

(*not comparable*)

- (mathematics, of a binary operation) Such that the order in which the operands are taken does not affect their image under the operation.
*Addition on the real numbers is commutative because for any real numbers , it is true that .*

- (algebra, of an algebraic structure) Having a commutative operation.
- (mathematics, of a diagram of morphisms) Such that any two sequences of morphisms with the same initial and final positions compose to the same morphism.