1. ## field

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.

However, the question goes on to ask,
If F has q elements, how many elements are in the group SL2(F)?

2. Originally Posted by PvtBillPilgrim
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.

However, the question goes on to ask,
If F has q elements, how many elements are in the group SL2(F)?
Think about it, what you actually want to know are the elements that are units. Our good friend rgep has given an exlanation here.

3. So it would just be:
((q^n)-1)*((q^n)-(q^n-1)) where n=2 in this case?

Thus, ((q^2)-1)*((q^2)-(q))

4. Originally Posted by PvtBillPilgrim
So it would just be:
((q^n)-1)*((q^n)-(q^n-1)) where n=2 in this case?

Thus, ((q^2)-1)*((q^2)-(q))
No!

$(q-1)(q^2-q)(q^3-q^2)....(q^n-q^{n-1})$
Or if you want to be cool

$\prod_{k=1}^n (q^{k}-q^{k-1})$

5. I don't know the dimension?