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16
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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 ![A^{-1} =\frac{1}{IAI} \left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right]](https://tex.z-dn.net/?f=%20%20A%5E%7B-1%7D%20%3D%5Cfrac%7B1%7D%7BIAI%7D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dd%26-b%5C%5C-c%26a%5C%5C%5Cend%7Barray%7D%5Cright%5D%20)