1. If B is formed from A by exchanging two rows then B is similar to A 2. If a triangular matrix is similar to diagonal, it is already diagonal 3. If A and B are diagonalizable so is AB 4. Every invertible matrix can be diagonalized My answers: 1. F: eigenvalues change, so the Jordan form would be different 2. I want to say true, but not entirely sure: eigenvalues would be the same and the jordan form is same so i guess that the triangular would be diagonal? 3. i would guess true, but not sure how to motivate 4. F, I know that for sure because we had an example in class [1 -1] [0 1] which is invertible but not diagonalizable since it has only 1 eigenvector, but how would I motivate it theoretically, i.e. how would I say in general that in certain cases there are not enough eigenvectors even for invertible matrices => not diagonalizable? Thanks!