# Definition of commutative in US English:

## commutative

Mathematics
• 1Involving 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 is a consequence of large rotations not being commutative in three dimensions, so the averages are not accurate in regions of high variability.’
• ‘In the density-independent case, this multiplication is commutative.’
• ‘So, the addition and multiplication we are used to using are commutative.’
• ‘In the 1840s, the Irish mathematician William Hamilton found that multiplication was not commutative in all number systems.’
• ‘An operation is commutative if you can change the order of the numbers involved without changing the result.’
1. 1.1rare Relating to or involving substitution or exchange.
• ‘The second difficulty was more damaging and, to a degree, commutative with the first.’
• ‘Of course, the relationship between painting and philosophy is not entirely commutative.’

### Origin

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).