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.
I made an "opposite" of that operation (like u subtraction is the "opposite" of adding, multiplying is the opposite of dividing, squaring is the opposite of square rooting, etc.) Let's say the opposite of # is @, so...
(A # B) # A = B (@ A to both sides) -->
A # B = B @ A (@ B to both sides) -->
A = (B @ A) @ B (# B to both sides) -->
B # A = B @ A (# A to both sides) -->
A # (B # A) = B
freaky solution
