If |a^2|=|b^2|, prove or disprove that |a|=|b|.
The hint I was given is that let a be an element of order 4n+2 and let the order of b=a2
The Attempt at a Solution
I can disprove this by looking at examples, such as in the group Z20 with letting a =2 and b=4, the |a|=10 and |b|=5, but |a^2|=5 and |b^2|=5. But I know that this does not disprove it for all groups, I need a more general solution. If anyone can help me on this it would be great.