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JCECE Engineering JCECE Engineering Solved Paper-2005

  • question_answer
    For non-singular square matrices \[A,\,\,\,B\] and \[C\] of the same order, \[{{(A{{B}^{-1}}C)}^{-1}}\]is equal to:

    A) \[{{A}^{-1}}B{{C}^{-1}}\]                              

    B) \[{{C}^{-1}}{{B}^{-1}}{{A}^{-1}}\]

    C) \[CB{{A}^{-1}}\]                               

    D) \[{{C}^{-1}}B{{A}^{-1}}\]

    Correct Answer: D

    Solution :

    Key Idea: If \[A\] and \[B\] are two non-singular matrices, then\[{{(AB)}^{-1}}={{B}^{-1}}{{A}^{-1}}\]. Since, \[A,\,\,\,B\] and \[C\] are the three non-singular matrices with same order. \[\therefore \]  \[{{(A{{B}^{-1}}C)}^{-1}}={{C}^{-1}}{{(A{{B}^{-1}})}^{-1}}\]                 \[={{C}^{-1}}B{{A}^{-1}}\]1


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