[1] Interchange leading diagonal elements:

`((2,-2),(-6,7))`

[2] Change signs of the other 2 elements:

`((2,2),(6,7))`

[3] Find |A|

Remember that our original matrix (from the question) is

`A=((7,-2),(-6,2))`

So the determinant of A is given by:

`|A|=|(7,-2),(-6,2)|=14-12=2`

[4] Multiply result of [2] by `1/|A|`

`A^-1=1/(|A|)((2,2),(6,7))`

`=1/2((2,2),(6,7))`

`=((1,1),(3,3.5))`

Is it correct?

Check:

`A^-1A=((1,1),(3,3.5))((7,-2),(-6,2))`

`=((7-6,-2+2),(21-21,-6+7))`

`=((1,0),(0,1))`

`=I`