JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Types of matrices, Algebra of matrices

  • question_answer
    If \[A=\left[ \begin{matrix}    0 & 1  \\    0 & 0  \\ \end{matrix} \right]\]and \[AB=O\], then B = [MP PET 1989]

    A) \[\left[ \begin{matrix}    1 & 1  \\    1 & 1  \\ \end{matrix} \right]\]

    B) \[\left[ \begin{matrix}    0 & 1  \\    -1 & 0  \\ \end{matrix} \right]\]

    C) \[\left[ \begin{matrix}    0 & -1  \\    1 & 0  \\ \end{matrix} \right]\]

    D) \[\left[ \begin{matrix}    -1 & 0  \\    0 & 0  \\ \end{matrix} \right]\]

    Correct Answer: D

    Solution :

    Since \[\left[ \begin{matrix}    0 & 1  \\    0 & 0  \\ \end{matrix} \right]\,\left[ \begin{matrix}    -1 & 0  \\    0 & 0  \\ \end{matrix} \right]=\left[ \begin{matrix}    0 & 0  \\    0 & 0  \\ \end{matrix} \right]=O=AB\] Þ \[B=\left[ \begin{matrix}    -1 & 0  \\    0 & 0  \\ \end{matrix} \right]\].


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