Why are these statements all true (a) If A is similar to B then A 2 is similar to B2

Chapter 6, Problem 20

(choose chapter or problem)

Why are these statements all true? (a) If A is similar to B then A 2 is similar to B2. (b) A2 and B2 can be similar when A and B are not similar (try A = 0,0). (c) [i ~] is similar to [i !]. (d) [i ~] is not similar to [i ~ ]. (e) If we exchange rows 1 and 2 of A, and then exchange columns 1 and 2, the eigenvalues ,stay the same. In this case M = __

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