I'm doing some exercises on group-theory but got stuck in the following question:
Let $G$ be a group such that for all $a \in G\setminus\{e\}$, $a^2 = e$. Prove that $|G|$ is even.
I tried using Lagrange's theorem but perhaps I still don't understand it fully for I was not capable of finishing it.
Could you shed some enlightenment on the matter?
Thanks in advance.