Think about it, what you actually want to know are the elements that are units. Our good friend rgep has given an exlanation here.
I have a question that I don't know the answer to.
Let F be a field. I showed that SL2(F) defined to be the matrix
(a b
c d) where a,b,c,d are in F and ad-bc=1 is a group.
I already proved that.
However, the question goes on to ask,
If F has q elements, how many elements are in the group SL2(F)?
I don't know the answer.