True or false a If A and B are similar matrices then Row A

True or false:

a) If A and B are similar matrices, then Row A = Row B

b) If A and B are similar matrices, then det A = det B

c) If A and B are n x n matrices such that det A = det B, then A and B have the same eigenvalues

d) If a set of 4 vectors spans R^4, then that set must be linearly independent

e) If = 0 is an eigenvalue of an n x n matrix A, then the columns of A are linearly independent

Solution

in the row equlient matrices rowA=rowBmmay not in similar matrces

b is true

c is true

d is true

e is false