A matrix A is called orthogonal if A-1 = AT. (a) Show that if A is an orthogonal matrix then det(A) = ±1. (b) Show that cos O sin 0 1 – sin 0 cos 0 is an orthogonal matrix. (c) Suppose that A and B are 3 × 3 matrices with det(A) = 2 and det(B) = -5. Find c E R such that det((cAT)-| B²AB¬!) = 7.

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