Question: Please explain fully so I can understand completely Let A be an n x n matrix. Prove that if a is an eigenvector of A

Please explain fully so I can understand completely

Let A be an n x n matrix. Prove that if a is an eigenvector of A corresponding to the eigenvalue 1, then x is also an eigenvector of A + cl, where c is a scalar. Moreover, find the corresponding eigenvalue of A + cI

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