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).