Let $\displaystyle G=\{z\in\mathbb{Z}: \ z^n=1, \ n\in\mathbb{N}\}$.

Prove $\displaystyle (G,*)$ is an abelian group under multiplication.

This makes sense since the units $\displaystyle \mathbb{Z}_p$ are group under multiplication.

$\displaystyle 1+0\mathbf{i}$ is the identity.

How do I find the inverse?