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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 21

  • question_answer
    If A and B are square matrices of the same order such that \[(A+B)(A-B)={{A}^{2}}-{{B}^{2}}\], then \[{{(AB{{A}^{-1}})}^{2}}=\]

    A) \[{{A}^{2}}{{B}^{2}}\]        

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

    C) \[{{B}^{2}}\]             

    D) I

    Correct Answer: C

    Solution :

    [c]: \[(A+B)(A-B)={{A}^{2}}-{{B}^{2}}\] \[\Rightarrow \]\[AA+BA-AB-BB={{A}^{2}}-{{B}^{2}}\] \[\Rightarrow \]\[{{A}^{2}}+BA-AB-{{B}^{2}}={{A}^{2}}-{{B}^{2}}\] \[\Rightarrow \]\[BA-AB=0\Rightarrow BA=AB\] \[\therefore \]\[{{(AB{{A}^{-1}})}^{2}}={{(BA{{A}^{-1}})}^{2}}={{(BI)}^{2}}={{B}^{2}}\]


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