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

  • question_answer
    If A is a square matrix, then which of the following matrices is not symmetric 

    A) \[A+{A}'\]

    B) \[A{A}'\]

    C) \[{A}'A\]

    D) \[A-{A}'\]

    Correct Answer: D

    Solution :

    Since\[{{A}_{21}}=1\], so it is symmetric. \[(A{A}'{)}'=({A}'{)}'{A}'=A{A}'\], so it is symmetric. \[({A}'A{)}'={A}'({A}'{)}'={A}'A\],  so it is symmetric. But\[(A-{A}'{)}'={A}'-A\ne A-{A}'\]. Hence it is not symmetric.


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