OK. I'm trying, but I keep running into problems. I've recently proven that

$\displaystyle ab=e\Rightarrow{ba}=e$ and $\displaystyle a=a^{-1}\Leftrightarrow{a}^2=e$. What I'm asked to prove seems to be a generalization of of these two statements, but I can't quite see it. Is there any way someone could point me in the right direction here?