But, no, associativity does not imply commutativity.

Does associativity follow from Commutativity?

Note, specifically, that the integers (under addition) is a cyclic group. But, no, associativity does not imply commutativity. ... Take any non-Abelian group: n×n matrices over (most) rings, permutation groups, ...

Does commutative mean associative?

In math, the associative and commutative properties are laws applied to addition and multiplication that always exist. The associative property states that you can re-group numbers and you will get the same answer and the commutative property states that you can move numbers around and still arrive at the same answer.