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

  • question_answer
    Which one of the following statements is true [MP PET 1996]

    A) Non- singular square matrix does not have a unique inverse

    B) Determinant of a non-singular matrix is zero

    C) If \[{A}'=A,\]then A is a square matrix

    D) If \[|A|\,\ne 0\], then \[|A.adj\,A|\,=\,|A{{|}^{(n-1)}}\], where \[A={{[{{a}_{ij}}]}_{n\times n}}\]

    Correct Answer: C

    Solution :

    If \[{A}'=A\], then order of \[{A}'\] will be same to order of A. So it is a square matrix.


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