1. The problem statement, all variables and given/known data Let R be the ring of all 2*2 matrices, over Zp, p a prime. Let G be the set of elements x in the ring R such that det x ≠ 0. Prove that G is a group. 2. Relevant equations Matrix is invertible in ring R. 3. The attempt at a solution Group properties and ring properties are similar I think. Group and Ring - closure, associativity, identity (zero in Rings?) Is this how I am supposed to approach the problem? By proving the common properties of a group and ring?