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  3. CEE Kerala Engineering

CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2001

  • question_answer
    If\[{{A}^{2}}-A+I=0,\]then the inverse of A is:

    A)  \[{{A}^{-2}}\]                   

    B)         \[A+I\]

    C)  \[I-A\] 

    D)         \[A-I\]

    E)  \[A\]

    Correct Answer: C

    Solution :

    \[\because \]\[{{A}^{2}}-A+I=0\] \[\Rightarrow \]               \[I=A-{{A}^{2}}\] \[\Rightarrow \]               \[{{A}^{-1}}I={{A}^{-1}}A-{{A}^{-1}}A.A\] \[\Rightarrow \]               \[{{A}^{-1}}=I-IA=I-A\]


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