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?
- (a)
- If \(A\) is similar to \(B\), then \(A^2\) is similar to \(B^2\). True False
- (b)
- If \(A^2\) is similar to \(B^2\), then \(A\) is similar to \(B\). True False
- (c)
- If \(A^T\) is similar to \(B\), then \(A\) is similar to \(B^T\). True False
- (d)
- If \(A\) is similar to \(B\), and \(B\) is similar to \(C\), then \(A\) is similar to \(C\). True False