Mark each of the following statements true or false:
(a) For all square matrices A, det(-A) = -det A.
(b) If A and B are n × n matrices, then det(AB) = det (BA).
(c) If A and B are n × n matrices whose columns are the same but in different orders, then det B = -det A.
(d) If A is invertible, then det(A-1) = det AT.
(e) If 0 is the only eigenvalue of a square matrix A, then A is the zero matrix.
(f) Two eigenvectors corresponding to the same eigenvalue must be linearly dependent.
(g) If an n × n matrix has n distinct eigenvalues, then it must be diagonalizable.
(h) If an n × n matrix is diagonalizable, then it must have n distinct eigenvalues.
(i) Similar matrices have the same eigenvectors.
(j) If A and B are two n × n matrices with the same reduced row echelon form, then A is similar to B.
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.