Let F be a finite field. Show that the product of all non-zero elements of F is -1.
An example of this is Wilson's Theorem.
The Attempt at a Solution
Let G be the multiplicative group of non-zero elements of F. Then G is cyclic. Let a be the generator of G. Here I get stuck. I thought that by just taking the product of each element represented by some power of the generator would be enough, but hey, it isn't. Not sure what to do now. Thnx for any help.