Linear Transformation Matrix: Inverse, Areas & Orientation Analysis

[12base]

Homework Statement

let f be the linear transformation represented by the matrix

M = ( -3, 2)
( 0, -2)

state what effect f has on areas, and whether f changes orientation.

Find the matrix that represents the inverse of f.

Homework Equations

N/A

The Attempt at a Solution

I think I'm over complicating this. I have drawn out the matrix on set of axes. I don't really understand the question, any help or pointers in the right direction would be greatly appreciated.

 

[CompuChip]

Since you have already calculated what M does to your axes (basis vectors), try figuring out what happens to a little square with corners on (0, 0) and (1, 1).

What happens to its area, for example? (At this point you may want to calculate the determinant of the matrix).

If you go from the x-axis to the y-axis you turn counterclockwise. Does the same hold for the transformed rectangle?