Let A and B be similar matrices. Let λ1, … λn be the (not necessarily distinct) eigenvalue...

Let A and B be similar matrices. Let λ1, … λn be the (not necessarily distinct) eigenvalues of A.

a) Prove that λ1 λ2… = det A.

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b) Conclude from the result of (a) that det A = det B.

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c) Prove that The number a11 + … + ann is called the trace of A.

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d) Prove from the result of (c) that A and B have equal traces.