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JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Special types of matrices, Transpose, Adjoint and Inverse of matrices

  • question_answer
    If \[{{A}^{2}}-A+I=0\], then \[{{A}^{-1}}\]= [Kerala (Engg,) 2001; AIEEE 2005]

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

    B) \[A+I\]

    C) \[I-A\]

    D) \[A-I\]

    Correct Answer: C

    Solution :

    \[{{A}^{2}}-A+I=0\] Þ  \[I=A-{{A}^{2}}\Rightarrow \]\[I=A(I-A)\] Þ  \[{{A}^{-1}}I={{A}^{-1}}(A(I-A))\] \[\Rightarrow \]  \[{{A}^{-1}}=I-A\].


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