Commutativity

In algebra, commutativity is a property of binary operations or of operators on a set. If $\star$ is a binary operation then the commutative property is the condition that

$x\star y=y\star x\,$

for all x and y. If this equality holds for a particular pair of elements, they are said to commute.

Examples of commutative operations are addition and multiplication of integers, rational numbers, real and complex numbers. In this context commutativity is often referred to as the commutative law.

See also

• Commutator
• Commutative diagram