In mathematics, the commutative property states that a binary operation on a set A is said to be commutative if for all in A we have . An example of a commutative operation is addition in the set of real numbers. When a group's operation is commutative, it is said to be abelian.
In layman's terms, an equation demonstrates commutativity when the constants or variables can be moved around an operation without changing the answer (e.g. 1 + 2 = 2 + 1 or 2 * 3 = 3 * 2). It is as if the numbers are "commuting" from one place to another. Thus, using real numbers, both multiplication and addition are commutative, and subtraction and division are not.
The commutative property
implies does not imply the associative property.