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]



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.

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



which simplifies to:



Edwin