Matrix \( \mathbf{A} \) is such that \( \mathbf{A}^{2}=2 \mathbf{A}...

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Matrix \( \mathbf{A} \) is such that \( \mathbf{A}^{2}=2 \mathbf{A}-\mathrm{I} \), where \( \mathrm{I} \) is the identity matrix. Then for \( n \geq 2, \mathbf{A}^{n}= \)
(A) \( n A-(n-1) I \)
(B) \( n \mathrm{~A}-\mathrm{I} \)
(C) \( 2^{n-1} \mathbf{A}-(n-1) I \)
(D) \( 2^{n-1} A-I \)
\( \mathrm{P} \)
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