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JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Self Evaluation Test - Determinats

  • question_answer
    If A is an orthogonal matrix of order 3 and \[B=\left[ \begin{matrix}    1 & 2 & 3  \\    -3 & 0 & 2  \\    2 & 5 & 0  \\ \end{matrix} \right],\] then which of the following is/are correct? 1. \[|AB|=\pm 47\] 2. \[AB=BA\] Select the correct answer using the code given below:

    A) 1 only

    B) 2 only

    C) Both 1 and 2     

    D) Neither 1 nor 2

    Correct Answer: C

    Solution :

    [c] The determinant of a orthogonal matrix is always \[\pm 1\] \[|A|=\pm 1\] \[B=\left[ \begin{matrix}    1 & 2 & 3  \\    -3 & 0 & 2  \\    2 & 5 & 0  \\ \end{matrix} \right]\] \[|B|=-10-2(-4)+3(-15)\] \[=-47\] \[|AB|=|A||B|\] \[=(\pm 1)(-47)\] \[=\pm 47\] Taking A as identity matrix we can prove\[AB=BA\]


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