Exercise 1 (On Similarity). Answer True or False. i) If A, B € Mnxn are similar then A? and B? are similar. ii) If A, B E Mnxn are similar then they have the same eigenvectors. iii) If A is an eigenvalue of A and A is invertible then A-' is an eigenvalue of A-. iv) If A1, B1 are similar and A2, B2 are similar with A1, B1, A2, B2 € Maxn then A1 + A2 is similar to B1 + B2. v) If A, B E Mnxn are similar then A' and B' are also similar.

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