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

  • question_answer
    The matrix \[A=\left[ \begin{matrix}    1 & -3 & -4  \\    -1 & \,\,\,3 & \,\,4  \\    1 & -3 & -4  \\ \end{matrix} \right]\] is nilpotent of index  [Kurukshetra CEE 2002]

    A) 2

    B) 3

    C) 4

    D) 6

    Correct Answer: A

    Solution :

    Since \[{{A}^{2}}=O\] (Zero matrix) and 2 is the least +ve integer for which \[{{A}^{2}}=O\]. Thus, A is nilpotent of index 2.


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