A) \[A+I\]
B) A
C) \[A-I\]
D) \[I-A\]
Correct Answer: D
Solution :
Given, \[{{A}^{2}}-A+I=O\] \[\Rightarrow \] \[{{A}^{-1}}{{A}^{2}}-{{A}^{-1}}.A+{{A}^{-1}}I=O\] \[\Rightarrow \] \[({{A}^{-1}}A).A-({{A}^{-1}}.A)+{{A}^{-1}}=0\] \[\Rightarrow \] \[A-I+{{A}^{-1}}=O\] \[\Rightarrow \] \[{{A}^{-1}}=I-A\]
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