Please help me solve following problem: (Same as Strang\'s problem 5.8 and 5.18, page 307) True or False. With reason if true and counter example if false: If B is formed from A by exchanging two rows, then B is similar to A. If a triangular matrix is similar to a diagonal matrix, it is already diagonal. If A and B are diagonalizable, so is AB. For every matrix A, there is a solution to du/dt = Au starting from u(0) = (1,..., 1). Every invertible matrix can be diagonalized. Every diagonalizable matrix can be inverted. Exchanging the rows of 2 by 2 matrix reverses the signs of its eigenvalues. Solution here are the answers a) t b) f c) t d) f e) t f) t g) f .

1. Please help me solve following problem:
(Same as Strang's problem 5.8 and 5.18, page 307) True or False. With reason if true and
counter example if false: If B is formed from A by exchanging two rows, then B is similar to A.
If a triangular matrix is similar to a diagonal matrix, it is already diagonal. If A and B are
diagonalizable, so is AB. For every matrix A, there is a solution to du/dt = Au starting from u(0)
= (1,..., 1). Every invertible matrix can be diagonalized. Every diagonalizable matrix can be
inverted. Exchanging the rows of 2 by 2 matrix reverses the signs of its eigenvalues.
Solution
here are the answers a) t b) f c) t d) f e) t f) t g) f