Let $G$ be a finite group, and the order of the group $G$, $|G|=r$.

For any $x \in G$, prove that $x^{-r}=e$ (where $e$ is a neutral in $G$).

Basically, I haven't tried anything except trying to manipulate the expression $aa^{-1}=e$ into what I'm trying to prove because I really have no idea what to do.

I would appreciate any hint, advice or etc. because I'm new in group theory and the concepts are still hard to understand.

Also, the next part of this task is this:

$G$ is a group such that $|G|=195$. Is there an element $g \neq e$ such that $g^{77}=e$?

Thanks in advance!