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2. (10pts) Suppose A is a 3 x 3 matrix such that det A=2. Find det B in each of the following cases: (a) B= -A(AT)A-1
8. Suppose that A and B are 3 x 3 matrices and that det(A) = }, det(B) = -1. Then det(-ABA adi(B)adi(A)) is (a) -27, (b) (c) -1, (d) 1 (e) None of the above.
3. Suppose that 2 and -5 are the only eigenvalues of the matrix A. Which of the following statements is true? A) 21 - A is invertible, and there is a nontrivial solution to Av = -5v. B) 21 - A is not invertible, and there is a nontrivial solution to Av = -5v. C) det(21 + A) = det(51 – A) = 0. D) det(21 + A) = 0, and there is a nontrivial solution to (51 – A)v = 0.