Prove each of the following statements. (a) Recall that a square invertible matrix is said to be orthogonal if AT = A-1. Suppose matrices B,C are orthogonal matrices of the same size. Prove that BC will also be an orthogonal matrix. %3D (b) Suppose that A is a square matrix with the property that A? = 0 Prove, using induction, (A+ I)" = nA+I for n > 1

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