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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2009

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

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

    B)  \[I\]

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

    D)  \[{{A}^{2}}\]

    Correct Answer: A

    Solution :

    Given,   \[(A+B)(A-B)={{A}^{2}}-{{B}^{2}}\] \[\Rightarrow \]  \[{{A}^{2}}-AB+BA-{{B}^{2}}={{A}^{2}}-{{B}^{2}}\] \[\Rightarrow \]               \[AB=BA\] Now,    \[{{(AB{{A}^{-1}})}^{2}}={{(BA{{A}^{-1}})}^{2}}={{B}^{2}}\]


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