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

  • question_answer
    If  A  and B  be symmetric matrices of the same order, then \[AB-BA\] will be a

    A) Symmetric matrix

    B) Skew symmetric matrix

    C) Null matrix

    D) None of these

    Correct Answer: B

    Solution :

    Since \[A,B\] are symmetric \[\Rightarrow \] \[A={A}'\] and \[B={B}'\] \[\therefore \] \[(AB-BA{)}'=(AB{)}'-(BA{)}'={B}'{A}'-{A}'{B}'\]                       \[=-({A}'{B}'-{B}'{A}')=-(AB-BA)\] \[\Rightarrow \] \[(AB-BA)\] is skew-symmetric.


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