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(7) Prove the following statements. (c) If A is invertible and similar to B, then B...

(7) Prove the following statements.

(c) If A is invertible and similar to B, then B is invertible and A−1 is similar to B−1 .

(d) The trace of a square matrix is the sum of the diagonal entries in A and is denoted by tr A. It can be verified that tr(F G)=tr(GF) for any two n × n matrices F and G. Prove that if A and B are similar, then tr A = tr B

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