Question: Suppose is an eigenvalue of a square matrix A with eigenvector X 0. Show that 3 - 2 + 3 is an eigenvalue

Suppose λ is an eigenvalue of a square matrix A with eigenvector X ≠ 0.
Show that λ3 - 2λ + 3 is an eigenvalue of A3 - 2A + 3I.

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