Matrix \( \mathrm{A} \) is such that \( \mathrm{A}^{2}=2 \mathrm{~A}-\mathrm{I} \), where \( \ma...
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0Matrix \( \mathrm{A} \) is such that \( \mathrm{A}^{2}=2 \mathrm{~A}-\mathrm{I} \), where \( \mathrm{I} \) is the identity matrix. Then for \( \mathrm{n} \geq 2, \mathrm{~A}^{\mathrm{n}}= \)
\( \mathrm{P} \)
(1) \( \mathrm{nA}-(\mathrm{n}-1) \mathrm{I} \)
(2) \( \mathrm{nA}-\mathrm{I} \)
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(3) \( 2^{n-1} A-(n-1) I \)
(4) \( 2^{n-1} \mathrm{~A}-\mathrm{I} \)
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