Since you have not specified the matrix I can only contribute some generalities; but I assume that aspecificmatrix needs to be considered in this exercise.

Consider the absolue value and the sign of the determinant of(a) state what effectfhas on areas, and whetherfchanges orientation.

Well, as I wrote, you need to tell us what happens to be.(b) Find the matrix that represents the inverse off.

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 imagef(ℓ) of the unit circle ℓ underf,in the form

ax²+ bxy + cy²= d

where a, b, c and d are integers.

See (a).(ii) What is the area enclosed byf(ℓ)?