Mathematics involving the condition that a group of quantities connected by operators gives the same result whatever the order of the quantities involved, e.g. .
This implies that is not commutative, since .
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).
From the OED on MacOS.