To find the inverse of a 2x2 matrix is easy:

1. Swap the elements in the main diagonal and change the signs 
   in the other.

2. Divide each element by the determinant of the matrix.

For your matrix,



1. Swap the red elements and change the signs of the green ones:



2. Now calculate the determinant of that matrix:



and divide every element by 



and reduce the fractions to lowest terms and simplify:



There are other ways to find the inverse of a 2x2 matrix,
but that's by far the easiest way. Unfortunately, larger 
matrices are not as easy to find the inverse of. 

Edwin