Let be an eigenvalue of . (a) is an eigenvalue of ? why or why not. (b) if is invertible, what can you say about an eigenvalue of that is related to , and why? hint: use definition to write , and then find a matrix to multiply this equation and see what happens. (c) let be m-by-n and be n-by-m, so that both are square matrices. show that if is an eigenvalue of , then it is also an eigenvalue of . hint: use definition to write , and then use a matrix to multiply this equation and see what happens. warning to (c): be careful with the definition which requires that an eigenvector be nonzero. in other words, if you claim a vector to be an eigenvector, you need to verity that it is not a zero vector. if in your proof the fact is not used, then the proof is incorrect, and there will be no credit given.