(Solution) - In each case assume that the transformation T is linear -(2025 Original AI-Free Solution)

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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 ?/4.
(d) T: (R2 ? R2 is counterclockwise rotation through ?/4.