To find an inverse matrix you first have to find the determinant and then put the absolute value of it under a 1. That's what is sitting outside in front of all those matrices. What you have to do now is multiply that determinant by what I teach to my students as the "mixed up matrix". They always remember from that. Change the position of the terms on the major axis (here they are a and d), and then switch the signs on the other 2 terms. Our inverse matrix then is [tex] A^{-1} =\frac{1}{IAI} \left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right] [/tex]
