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Why det a is the product of the n eigenvalues of a

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Reference no: EM131555531

Question: Let A be an n X n matrix, and suppose A has n real eigenvalues, λ1,,,,,,,,, λn, repeated according to multiplicities, so that

det (A - λI) = (λ1 - λ) (λ2 - λ). . .(λn - λ)

Explain why det A is the product of the n eigenvalues of A. (This result is true for any square matrix when complex eigenvalues are considered.)

Reference no: EM131555531

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