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BCECE Engineering BCECE Engineering Solved Paper-2002

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

    A) \[{{A}^{-1}}\]                                    

    B)  \[A+I\]

    C)         \[I-A\] 

    D)         \[A-I\]

    Correct Answer: C

    Solution :

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


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