If \(A=\begin{bmatrix}1&2\\3&4\end{bmatrix}\) satisfies \(A^2-5A-2I=O\), then \(A^{-1}\) equals
A. \(\frac12(A-5I)\)
B. \(\frac15(A-5I)\)
C. \(2(A-5I)\)
D. \(\frac12(5I-A)\)
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Answer: A. \(\frac12(A-5I)\)
\(A(A-5I)=2I\Rightarrow A^{-1}=\frac12(A-5I)\).
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· 23 Oct 2026
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