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

  • question_answer
    For any square matrix A, \[A{{A}^{T}}\]is a [RPET 2000]

    A) Unit matrix

    B) Symmetric matrix

    C) Skew symmetric matrix

    D) Diagonal matrix

    Correct Answer: B

    Solution :

    We have,\[{{A}^{100}}={{2}^{99}}\left[ \begin{matrix}    1 & 1  \\    1 & 1  \\ \end{matrix} \right]\]\[=A{{A}^{T}}\](by reversal law) \ \[A{{A}^{T}}\] is symmetric matrix.


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