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

freaky solution by Victor Zapana)

Your proof has a serious problem. Given only the information in the problem, it is not guaranteed that an inverse operator (your @) even exists.

Also, when you apply # B to each side (from line 3 to 4 in your proof), you assumed the commutative property was true and put B on the left.