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

  • question_answer
    If \[A=\left[ \begin{matrix}    1 & 2 & 3  \\    5 & 0 & 7  \\    6 & 2 & 5  \\ \end{matrix} \right]\]and \[B=\left[ \begin{matrix}    1 & 3 & 5  \\    0 & 0 & 2  \\ \end{matrix} \right]\], then which of the following is defined

    A) AB

    B) \[A+B\]

    C) \[{A}'{B}'\]

    D) \[{B}'{A}'\]

    Correct Answer: C

    Solution :

    By inspection, \[{A}'\]is a matrix of order 3 × 3 and \[{B}'\]is a matrix of order 3× 2. Therefore multiplication of these matrices is defined.


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