1. The problem statement, all variables and given/known data Let G be a finite group in which every element has a square root. That is, for each x in G, there exists a y in G such that y^2=x. Prove every element in G has a unique square root. 2. Relevant equations G being a group means it is a set with operation * satisfying: 1.) for all a,b,c in G, a*(b*c)=(a*b)*c 2.) there exists an e s.t. for all x in G, x*e=x 3.) for all x in G there exists an x' s.t. x'*x=e 3. The attempt at a solution The only thing I have gotten so far is the reason why (-2)^2 and 2^2 both equaling 4 doesn't present a counterexample. The reason it doesn't is because (-2) has no square root so it is not in our group G. ... other than that I'm stuck..