1. The problem statement, all variables and given/known data If |a^2|=|b^2|, prove or disprove that |a|=|b|. 2. Relevant equations |x| means the order of the element x. 3. The attempt at a solution Let consider the group Z20. |a^2|=|b^2| when a = 2 and b = 4 (since the order of 4 and 8 are both 5 in z20). But |2| does not equal the order of 4 in Z20. But I know that this is not enough, due to that the problem, does not give us anything about the group or the elements of the group. Plus I think I am certain that i need to generalize more instead of giving just one example. If anyone got any advice for me on this, it would be great.