Every prime field of finite characteristic $p$ is isomorphic to the field $\mathbb Z_{p}$ of the residue classes of the set of integers modulo $p$.

Question

All I know about this is $\Bbb Z_{p}$ is a field of order $p$. Therefore,if $e\neq a \in \Bbb Z_{p}$,then $\vert a \vert =p$.But I'm not getting any idea of how to move further. Any kind of hints are welcome.

Thank You.