# Does commutativity imply Associativity?

Does commutativity imply associativity? I’m asking this because I was trying to think of structures that are commutative but non-associative but couldn’t come up with any. Are there any such examples?

NOTE: I wasn’t sure how to tag this so feel free to retag it.

Consider the operation $(x,y) \mapsto xy+1$ on the integers.