Proof in modern algebra. Prove $(n-1)! = -1 (textrm{mod n})$ iff n is prime

Prove $(n-1)! = -1 \ (\textrm{mod n})$ iff n is prime

I can understand how the first part of the proof $(n-1)!=-1 \ (\textrm{mod n})$ is true if n is prime simply by testing it out. However, I'm unsure of how to go about proving it.