# commutative

Mathematicsinvolving the condition that a group of quantities connected by operators gives the same result whatever the order of the quantities involved, e.g. $a\times b=b\times a$.

This implies that $\frac{a}{b}$ is not commutative, since $\frac{a}{b}\ne \frac{b}{a}$.

mid 16th century (in the sense ‘relating to transactions between people’): from French commutatif, -ive or medieval Latin commutativus, from commutat- ‘exchanged’, from the verb commutare (see commute).