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 My solution
Your solution assumes the commutative property is true. You cannot assume that from what the problem tells you.