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12th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-5

  • question_answer
    A is a matrix such that \[{{\mathbf{A}}^{\mathbf{3}}}=\mathbf{I}\], then \[{{\mathbf{A}}^{-\mathbf{1}}}\]=

    A)   A                   

    B)  A2             

    C)  A3                               

    D)  None of these

    Correct Answer: B

    Solution :

    [b] \[\because {{A}^{3}}=1\] Multiplying by \[{{A}^{-1}}\]on both sides, we have \[{{A}^{3}}.\text{ }{{A}^{-1}}=1.\text{ }{{A}^{-1}}\] \[\Rightarrow {{A}^{2}}.\left( A-{{A}^{-1}} \right)={{A}^{-1}}\]   \[\Rightarrow {{A}^{2}}.1={{A}^{-1}}\] \[\Rightarrow {{A}^{2}}={{A}^{-1}}\] Hence, option [b] is correct.


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