Since you have not specified the matrix I can only contribute some generalities; but I assume that a specific matrix needs to be considered in this exercise.
Consider the absolue value and the sign of the determinant of(a) state what effect f has on areas, and whether f changes orientation.
Well, as I wrote, you need to tell us what happens to be.(b) Find the matrix that represents the inverse of f.
If the inverse image must satisfy . Now express in terms of according to your solution of (b).(c) (i) Use the matrix that you found in part (b) to find the image f(ℓ) of the unit circle ℓ under f, in the form
ax² + bxy + cy² = d
where a, b, c and d are integers.
See (a).(ii) What is the area enclosed by f(ℓ)?