Question: Let L: R2 R2 be defined by L(x) = Ax, for x in R2, where A is an orthogonal matrix? (a) Prove that if

Let L: R2 → R2 be defined by L(x) = Ax, for x in R2, where A is an orthogonal matrix?
(a) Prove that if det(A) = 1, then L is a counterclockwise rotation?
(b) Prove that if det(A) = -1, then L is a reflection about the x-axis, followed by a counterclockwise rotation?

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