Answer
(a) 3
(b) −1
(c) −48
(d) −9
(e) −3
Work Step by Step
(a) det(AB) = det(A) det(B) = (−3)(−1) = 3
(b) det(B^5) = (det B)^5 = (−1)^5 = −1
(c) det(2A) = 2^4 det(A) = (16)(−3) = −48
(d) det(A^tBA) = det(A^t) det(B) det(A) = det(A) det(B) det(A) = (−3)(−1)(−3) = −9
(e) det(B^−1AB) = det(B^−1) det(A) det(B) = ((det B)^−1)(−3)(−1) = (1/−1)(−3)(−1) = −3
