For matrices \(A\), \(B\) and \(C\). True or False? If False, you should come up with a counterexample. If True, can you give a proof?

1.
If \(A\) is similar to \(B\), then \(A^2\) is similar to \(B^2\).
True False
2.
If \(A^2\) is similar to \(B^2\), then \(A\) is similar to \(B\).
True False
3.
If \(A^T\) is similar to \(B\), then \(A\) is similar to \(B^T\).
True False
4.
If \(A\) is similar to \(B\), and \(B\) is similar to \(C\), then \(A\) is similar to \(C\).
True False