Find and example of two elements $a,b$ in a finite group $G$ such that $|a| = |b| = 2, a \ne b$ and $|ab|$ is odd. Find and example of two elements $a,b$ in a finite group $G$ such that $|a| = |b| = 2, a \ne b$ and $|ab|$ is odd. Any ideas as to how I would go about finding it?
Thanks

In $S_3$ the multiplication of $(a,b)$ and $(b,c)$ is $(a,b,c)$
