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  3. RAJASTHAN ­ PET

RAJASTHAN ­ PET Rajasthan PET Solved Paper-2002

  • question_answer
    If\[{{A}^{3}}=I\]for any matrix A, then\[{{A}^{-1}}\]is equal to

    A)  \[{{A}^{2}}\]              

    B)  A

    C)  \[{{A}^{3}}\]             

    D)  None of these

    Correct Answer: A

    Solution :

     \[{{A}^{3}}=I\] \[\Rightarrow \] \[A.{{A}^{2}}=I\] \[\Rightarrow \] \[{{A}^{-1}}A.{{A}^{2}}={{A}^{-1}}\] \[\Rightarrow \] \[{{A}^{2}}={{A}^{-1}}\]


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