(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

The hint I was given is that let a be an element of order 4n+2 and let the order of b=a2

3. 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Abstract algebra

**Physics Forums | Science Articles, Homework Help, Discussion**