Question: 5. Let A be an n x n matrix. (a) (5pts) Show that if A is an orthogonal matrix, then det (A) = +1. (b)

5. Let A be an n x n matrix. (a) (5pts) Show that if A is an orthogonal matrix, then det (A) = +1. (b) (5 pts) Show that if A * 0 and A3 = 0, then A is not diagonalizable. (Hint: Assume A is diagonalizable and then get a contraction. )

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