JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Expansion of determinants, Solution of equation in the form of determinants and properties of determinants

  • question_answer
    \[\left| \begin{matrix}    0 & a & -b  \\    -a & 0 & c  \\    b & -c & 0  \\ \end{matrix} \right|=\] [MP PET 1992]

    A) \[-2abc\]

    B) \[abc\]

    C) 0

    D) \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}\]

    Correct Answer: C

    Solution :

    \[\left| \,\begin{matrix}    0 & a & -b  \\    -a & 0 & c  \\    b & -c & 0  \\ \end{matrix}\, \right|\] = 0 (Since value of determinant of skew-symmetric matrix of odd orders is 0).


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