I would be really grateful if you could help me out on these tricky questions.
Let f be the linear transformation represented by the matrix M =
(a) state what effect f has on areas, and whether f changes orientation.
(b) Find the matrix that represents the inverse of f.
(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.
(ii) What is the area enclosed by f(ℓ)?
Anyone who can shed some light will receive my eternal gratitude!