Let \( A \) be an \( n \times n \) matrix such that \( A^{n}=\alpha...

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Let \( A \) be an \( n \times n \) matrix such that \( A^{n}=\alpha A \) where \( \alpha \) is a real number different from 1 and \( -1 \). Prove that the matrix \( A+I_{n} \) is invertible.
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