# Math Help - prove or disprove?

1. ## prove or disprove?

If |a^2|=|b^2|, prove or disprove that |a|=|b|

2. Originally Posted by mandy123
If |a^2|=|b^2|, prove or disprove that |a|=|b|
No. Consider $G = S_6$. Let $a=(123456)$ and $b=(123)(456)$. Now $|a| = 6$ and $|a^2| = 3$. While $|b| = 3$ and $|b^2| = 3$.