Question 258490
<pre><font size = 4 color = "indigo"><b>
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,

{{{(matrix(2,2,
red(-9), green(5),
 green(6), red(3)))}}}

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

{{{(matrix(2,2,
red(3), green(-5),
 green(-6), red(-9)))}}}

2. Now calculate the determinant of that matrix:

{{{abs(matrix(2,2,
red(3), green(-5),
 green(-6), red(-9)))= (red(3))*(red(-9))-(green(-5))*(green(-6))=(-27)-(30)=-57  }}}

and divide every element by {{{-57}}}

{{{(matrix(2,2,
red(3)/(-57), green(-5)/(-57),
 green(-6)/(-57), red(-9)/(-57)))}}}

and reduce the fractions to lowest terms and simplify:

{{{(matrix(2,2,
-1/19, 5/57,
 2/19, 3/19))}}}

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</pre>