1. The problem statement, all variables and given/known data Prove that (a b c d) is a unit in the ring M(R) if and only if ad-bc !=0. In this case, verify that its inverse is (d/t -b/t -c/t a/t) where t= ad-bc. 2. Relevant equations An element a in a ring R with identity is called a unit if there exists u in R s.t. au = 1 = ua (where 1 is the identity of the ring). In thise case the element u is called the multiplicative inverse of a and is denoted a^-1. 3. The attempt at a solution I took an arbitrary element from M(R) 2x2, say (e f g h) and I know that if I multiply my unit times that, then I should get the identity matrix. (a b x (e f ) = (1 0 c d) . g h ) . 0 1) which gives me four equations ae + bg = 1 ; ce + dg = 0 af + bh = 0 ; cf + dh = 1 This is where I became lost. I started substituting things, and it became a mess. I guess this question is really about showing where the determinant comes from. Please help, thank you.