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,. Show that if det(a b c d) = ad - bc ≠ 0, then (a b c d) is invertible in R. 2. Relevant equations 3. The attempt at a solution I don't know how to start if Zp, with p a prime, is the clause. I know that since ad- bc ≠ 0, it automatically makes the matrix (a b c d) invertible in R.. but does the determinant have to be one?