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12th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-7

  • question_answer
    If A is the square matrix such that \[{{A}^{2}}=I\] (where I =identity matrix), then \[{{\mathbf{A}}^{-\mathbf{1}}}=\]

    A)  A                                

    B)  2A           

    C)  \[A+1\]                       

    D)  None of these

    Correct Answer: A

    Solution :

    [a] \[\because {{A}^{2}}=I\] Multiplying \[{{A}^{-1}}\]on both sides, we have \[\because A.{{A}^{-1}}=I.{{A}^{-1}}\] \[\Rightarrow A.\left( A\text{ }{{A}^{-1}} \right)={{A}^{-1}}\] [\[\therefore A\] is a square matrix] \[\Rightarrow A.I={{A}^{-1}}\] \[\Rightarrow A={{A}^{-1}}\] Hence, option [a] is correct.


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