In mathematics, especially abstract algebra, a binary operation * on a set

*S*is

**commutative**if, for all

*x*and

*y*in

*S*,

*x**

*y*=

*y**

*x*.

The most commonly known examples of commutativity are addition and multiplication of natural numbers; for example:

- 4 + 5 = 5 + 4 (since both expressions evaluate to 9)
- 2 × 3 = 3 × 2 (since both expressions evaluate to 6)

An Abelian group is a group whose operation is commutative.

A ring is called commutative if its multiplication is commutative, since the addition is commutative in any ring.

See also: Associativity, Distributive property