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Question 4.E.8.9: If A ≃ B, show that A^k ≃ B^k for all nonnegative integers k......

If A \simeq B, show that A^k \simeq B^k for all nonnegative integers k.

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B = P^{−1}AP \Longrightarrow B^k = P^{−1}APP^{−1}AP· · ·P^{−1}AP = P^{−1}AA· · ·AP = P^{−1}A^kP

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