I am new to linear algebra, and am unsure re the following question:
True or False?
Let A and B be matrices of n x n.
If A and B are diagonalizable and they have the same characteristic polynomial, then A and B are similar.
If A and B are row equivalent and A is diagonalizable, then B is diagonalizable.
My intuitive answer is "false" to 1, and "true" to 2.
However, I am not sure, and either way, I would ideally like to be able to prove it...