Return to Glossary.

**Formal Definition**

A binary operation $*$ on a set $S$ is **commutative** if, for all $a,b\in S$, $a*b=b*a$

**Informal Definition**

If binary operation yields the same output for any given pair of inputs in its domain, regardless what the order of the inputs is, the operation is commutative.

**Example(s)**

Addition is a commutative binary operation. This is illustrated by fact that, $1+2=2+1=3$.

Multiplication is a commutative binary operation. This is illustrated by fact that $5\times 4 = 4\times 5=20$

**Non-example(s)**

Subtraction is an example of a binary operation that is not commutative. For example, $2-1$ is not equal to $1-2$.

**Additional Comments**

Add any other comments you have about the term here