So I am asked to proof the following
If p is a prime and b is a non zero element of the field $\mathbb{Z}_{p}$.
Show that $b^{p-1}=1$
The hint is Lagrange.
I didn't proof it, but I think I should start by noting that.
Since $\mathbb{Z}_{p}$ is a field all of its non zero elements have multiplicative inverse. And then somehow I should connect what I know about fields, and Lagranges theorem which states that the order of a subgroup divides the order of the Group. But I am not sure how to connect it