Does commutativity imply associativity?

From: Brian Smith (brianscsmith_at_yahoo.com)
Date: 08/27/04 

Date: 27 Aug 2004 15:35:32 -0700

I know that there are mathematical objects which are associative but
not commutative with respect to some binary operation. Matrix
multiplication is an example, associative but not commutative.

My question is: Is there some set of objects which is commutative but
not associative with respect to some binary operation, or does
commutativity imply associativity?

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