In each case assume that the transformation T is linear, and use Theorem 2 to obtain the

Question:

In each case assume that the transformation T is linear, and use Theorem 2 to obtain the matrix A of T.
(a) T": R2 → R2 is reflection in the line y = -x.
(b) T: R2 → R2 is given by T(X) = -X for each X in R2.
(c) T: R2 → R2 is clockwise rotation through π/4.
(d) T: (R2 → R2 is counterclockwise rotation through π/4.