Show that if A and B are two nxn martices that both have the same diagonalizing matrix X, then BA=BA?

Answer 1

Well BA=BA all of the time.

I think you mean BA=AB.

You want to use the fact that if two matrices have the same diagonalizing matrix, then they are similar. Since they are similar, you have that A=P^{-1}BP and also PAP^{-1}=B.

Now use substitution into BA and AB and show that you get the same thing.