(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Homework Help: Element order proof, need help!

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