Assume all matrices are square. If A is similar to B, then A^2 is similar to B^2. I need to prove or disprove.
I know that to be similar there needs to exist a nonsingular matrix S such that A = S^(-1)BS.
I want to say that it will be true:
AA = [S^(-1)BS][S^(-1)BS] = S^(-1)BBS
A^2 = S^(-1)B^2S
Therefore, A^2 is similar to B^2
Can someone let me know if I am correct and if not, help me out?