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JEE Main & Advanced Sample Paper JEE Main Sample Paper-34

  • question_answer
    Let \[A=\left( \begin{matrix}    1 & 2  \\    3 & 4  \\ \end{matrix} \right)\] and \[B=\left( \begin{matrix}    a & 0  \\    0 & b  \\ \end{matrix} \right)\] where \[a,b\in N\]Then  

    A)  there cannot exist any B such that AB = BA.

    B)  there exist more than one but finite number     of B's such that AB=BA.               

    C)  there exists exactly one B such that AB = BA.

    D)  there exist infinitely many B's such that AB

    Correct Answer: D

    Solution :

    \[A=\left( \begin{matrix}    1 & 2  \\    3 & 4  \\ \end{matrix} \right),B=\left( \begin{matrix}    a & 0  \\    0 & b  \\ \end{matrix} \right)\]             Now, \[AB=BA\,\Rightarrow \] when a = b


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