Question 1164041
<pre>
{{{A = (matrix(2,2,9,-8,3,16))}}}

First swap the upper left and lower right diagonal elements

{{{(matrix(2,2,16,-8,3,9))}}}

Change the signs of upper right and lower left diagonal elements

{{{(matrix(2,2,16,8,-3,9))}}}

Calculate the determinant of the original matrix, [or the determinant of
either of these, as they all have the same determinant:

(9)(16)-(-8)(3) = 144-(-24) = 144+24 = 168

Divide each term by the value of the determinant

{{{(matrix(2,2,16/168,8/168,-3/168,9/168))}}}

Reduce any fractions that will reduce (they all will)

{{{A^(-1)=(matrix(2,2,2/21,1/21,-1/56,3/56))}}}

This method works ONLY for 2x2 matrices.

Edwin</pre>