Question

Which of the following represents the inverse of the matrix below?

Answer 1

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 $A^{-1} =\frac{1}{IAI} \left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right]$