Hi

Please help me with this abstract algebra problem.

Let G be the set of all 2X2 matrices such that it's elements are integers modulo p, p is a prime number.

Determinant of matrix is not zero.

It is given that G forms a non-abelian finite group.

The question is for any prime p, what is the order of G.

e.g. in special case of p = 3 , order is 48.

If it helps, this is problem # 2.2.9 from Topics in Algebra (Herstein book second edition).