Let (G,*) be a finite group with an even number of elements. Show that there must exist at least one element $\displaystyle a \neq e \in G$ such that $\displaystyle a^2=e$.

I have no clue how to start and what ticks me off about that is that I think I've seen it before. (And I don't recall it was that difficult, either.) However my class notes (from years ago) doesn't contain the proof. :rolleyes:

-Dan