Let A and B be 6 x 6 matrices, with det A = -10 and det...

   

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Let A and B be 6 x 6 matrices, with det A = -10 and det B = 5. Use properties of determinants to compute: a) det(3A) b) det (ATB) Part II. Indicate whether the statements are true or false. (To be true, they must always be true.) Add a counterexample if false and a reason if true. -1 a) If A and B are invertible 22 matrices, then (AB) = A b) If P and D are n x n matrices, then det(P DP 1) = det(D) c) If A is a matrix with two identical rows, then det(A) = 0. d) det(A+B) = det(A) + det(B) Let A and B be 6 x 6 matrices, with det A = -10 and det B = 5. Use properties of determinants to compute: a) det(3A) b) det (ATB) Part II. Indicate whether the statements are true or false. (To be true, they must always be true.) Add a counterexample if false and a reason if true. -1 a) If A and B are invertible 22 matrices, then (AB) = A b) If P and D are n x n matrices, then det(P DP 1) = det(D) c) If A is a matrix with two identical rows, then det(A) = 0. d) det(A+B) = det(A) + det(B)

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a det3A 36detA 729detA 72910 7290 b detAT B detAdetB detA1detB detAdetB 105 2 ... View the full answer