Hi guys, can anybody see whether my intuition is correct?

True or False?

Let A and B be matrices of n x n.

1. If A and B are diagonalizable and they have the same characteristic polynomial, then A and B are similar.

2. 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...

Many thanks!

True or False?

Let A and B be matrices of n x n.

1. If A and B are diagonalizable and they have the same characteristic polynomial, then A and B are similar.

2. 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...

Many thanks!

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