You have matrix A: [ a b ] [ ] [ c d ] and you want to find matrix Z so that AZ = I; that is, you want to find p, q, r, and s, so that [ a b ] [ p q ] [ 1 0 ] [ ] [ ] = [ ] [ c d ] [ r s ] [ 0 1 ] Now how do you do that? You know how to multiply matrices, so multiply the two on the left. Let me know when you've done that. You got: [ ap+br aq+bs ] [ 1 0 ] [ ] = [ ] [ cp+dr cq+ds ] = [ 0 1 ] Now we can equate the elements on the left and right sides, which gives us four equations in the unknowns p, q, r, and s: ap + br = 1 aq + bs = 0 cp + dr = 0 cq + ds = 1 Now solve the four equations for p, q, r, and s, in terms of a, b, c, and d, and let me know what you get.