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

  • question_answer
    If \[A=\left[ \begin{matrix}    0 & 1  \\    0 & 0  \\ \end{matrix} \right],\]I is the unit matrix of order 2 and a, b are arbitrary constants, then \[{{(aI+bA)}^{2}}\]is equal to [RPET 1992]

    A) \[{{a}^{2}}I+abA\]

    B) \[{{a}^{2}}I+2abA\]

    C) \[{{a}^{2}}I+{{b}^{2}}A\]

    D) None of these

    Correct Answer: B

    Solution :

    \[{{(aI+bA)}^{2}}=\left[ \begin{matrix}    a & b  \\    0 & a  \\ \end{matrix} \right]\,\left[ \begin{matrix}    a & b  \\    0 & a  \\ \end{matrix} \right]=\left[ \begin{matrix}    {{a}^{2}} & 2ab  \\    0 & {{a}^{2}}  \\ \end{matrix} \right]={{a}^{2}}I+2abA\].


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