Consider a binary operation # that is closed under the set of integers (if a and b are integers, then a#b is an integer).

Assume that, for all integers a and b, it is true that (a#b)#a=b.

Prove that a#(b#a)=b.

(In reply to re(2): A simple solution by Charlie)

Commutativity is a property of an operation, not of the set of real numbers, as someone suggested. The point of the problem is that you can't assume anything about the given operation other than what's stated in the problem, so arguments about commutativity, associativity, inverses, anything that applies to 'normal' operations do not necessarily apply here.
Charlie's first suggestion shows the only valid way to prove this.

Posted by DJ on 2003-10-19 22:08:41