Question 519652
<pre>
The rule for finding the inverse of a 2x2 matrix:

1. Swap the upper left and lower right elements.
2. Change the signs of the upper right and lower left elements.
3. Divide each element by the determinate of the matrix.  

[Note: It doesn't matter whether you use the determinant of the original
 matrix or the altered one after step 2, since they have the same determinant]

{{{(matrix(2,2,6,2,8,3))}}}

1. Swap the upper left and lower right elements.

{{{(matrix(2,2,3,2,8,6))}}}

2. Change the signs of the upper right and lower left elements.

{{{(matrix(2,2,3,-2,-8,6))}}}

3. Divide each element by the determinate of the matrix.

The determinant of the original matrix is 6×3-2×8 = 18-16 = 2
[Note: that's the same as 3×6-(-2)(-8)=18-16 = 2]

You get

{{{(matrix(2,2,3/2,(-2)/2,(-8)/2,6/2))}}}

which simplifies to:

{{{(matrix(2,2,3/2,-1,-4,3))}}}

Edwin</pre>