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JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Mock Test - Matrices

  • question_answer
    If A and B are two nonsingular matrices of the same order such that B?=I, for some positive integer r>1, then \[{{A}^{-1}}{{B}^{\,r-1}}A-{{A}^{-1}}{{B}^{-1}}A\]=

    A) I                    

    B) 2I

    C) O            

    D) -I

    Correct Answer: C

    Solution :

    [c] Given \[{{B}^{r}}=I\]or \[{{B}^{r}}{{B}^{-1}}\]\[=I{{B}^{-1}}\]or \[{{B}^{r-1}}={{B}^{-1}}\] \[\Rightarrow {{A}^{-1}}{{B}^{r-1}}A-{{A}^{-1}}{{B}^{-1}}A\] \[={{A}^{-1}}{{B}^{-1}}A-{{A}^{-1}}{{B}^{-1}}A=O\]


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