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

  • question_answer
    If \[A=\left[ \begin{matrix}    -1 & 0 & 0  \\    0 & -1 & 0  \\    0 & 0 & -1  \\ \end{matrix} \right]\], then \[{{A}^{2}}\]is  [MNR 1980]

    A) Null matrix

    B)  Unit matrix

    C)   A

    D) 2A

    Correct Answer: B

    Solution :

    \[{{A}^{2}}=\left[ \begin{matrix}    -1 & 0 & 0  \\    0 & -1 & 0  \\    0 & 0 & -1  \\ \end{matrix} \right]\,\left[ \begin{matrix}    -1 & 0 & 0  \\    0 & -1 & 0  \\    0 & 0 & -1  \\ \end{matrix} \right]=\left[ \begin{matrix}    1 & 0 & 0  \\    0 & 1 & 0  \\    0 & 0 & 1  \\ \end{matrix} \right]=I\].


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