Finding an inverse of a Matrix

For a 2x2 Matrix I have.. 6 - 1
3 -2

When I use my calculator and row operations I get.. 2/9 -1/9
1/3 -2/3

But my class got - 2 1
- 3 6

? Who is correct?

(6 -1)..(2/9 -1/9)
(3 -2)*.(1/3 -2/3) =

(12/9 - 1/3) (-6/9 + 2/3)
(6/9 - 2/3) (-3/9 + 4/3)

=

(1 0)
(0 1), this is correct!

Now, you must do the problem by hand!