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
A simple solution by Angela)
In reply to Angela, and to Iggyb387. This is not the commutative property (although, the relation *might* be commutative).
Commutative means that (a#b)#c = a#(b#c). This is not a given in the original problem. Therefore, we cannot use the commutative property.
And if the relation has the transitive property, this means that if a#b and b#c, then a#c. Again, this is not guaranteed by original problem.
--- SK
re: A simple solution
