For square matrices \(A\) and \(B\). True or False? If False, you should come up with a counterexample. If True, can you give a proof?
- (a)
- If \(\lambda \) is an eigenvalue of \(A\), then \(-\lambda \) is an eigenvalue of \(A^{-1}\). True False
- (b)
- If \(\lambda \) is an eigenvalue of \(A\), then \(\lambda - c\) is an eigenvalue of \(A - cI\). True False
- (c)
- If \(\lambda \) is an eigenvalue of \(A\), then \(2\lambda \) is an eigenvalue of \(2A\). True False