JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Special types of matrices, Transpose, Adjoint and Inverse of matrices

  • question_answer
    For two invertible matrices A and B  of suitable orders, the  value of \[{{(AB)}^{-1}}\]is [Pb. CET 2000, RPET 2000, 02; Karnataka CET 2001]

    A) \[{{(BA)}^{-1}}\]

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

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

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

    Correct Answer: B

    Solution :

    Given, Square matrices A and B of same order. We know that if A and B are non-singular matrices of the same orders, then \[{{(AB)}^{-1}}={{B}^{-1}}{{A}^{-1}}.\]


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