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

  • question_answer
    If \[A=[a\,\,b],B=[-b-a]\]and \[C=\left[ \begin{align}   & \,\,\,\,a \\  & -a \\ \end{align} \right]\], then the correct statement is [AMU 1987]

    A) \[A=-B\]

    B) \[A+B=A-B\]

    C) \[AC=BC\]

    D) \[CA=CB\]

    Correct Answer: C

    Solution :

    \[AC=[a\,\,\,b]\,\,\left[ \begin{align}   & \,\,\,a \\  & -a \\ \end{align} \right]=[{{a}^{2}}-ab]\] \[BC=[-b\,\,\,-a]\,\left[ \begin{align}   & \,\,\,a \\  & -a \\ \end{align} \right]=[{{a}^{2}}-ab]\] \ \[AC=BC\].


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