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. a × b = b × a .

This implies that a b is not commutative, since a b 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).

From the Oxford Dictionary of English (ODE) on macOS.

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