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

  • question_answer
    \[A=\left[ \begin{matrix}    4 & 6 & -1  \\    3 & 0 & 2  \\    1 & -2 & 5  \\ \end{matrix} \right]\],\[B=\left[ \begin{matrix}    2 & 4  \\    0 & 1  \\    -1 & 2  \\ \end{matrix} \right],\,\,C=\left[ \begin{matrix}    3  \\    1  \\    2  \\ \end{matrix} \right]\], then the expression which is not defined is [MP PET 1987]

    A) \[{{A}^{2}}+2B-2A\]

    B) \[C{C}'\]

    C) \[{B}'C\]

    D) \[AB\]

    Correct Answer: A

    Solution :

    By inspection, \[{{A}^{2}}\]and A matrix is of order\[3\times 3\], while B matrix is of order\[3\times 2\]. Therefore, \[{{A}^{2}}+2B-2A\] is not defined. 


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