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

  • question_answer
    \[A,B\] are n-rowed square matrices such that \[AB=O\]and B is non-singular. Then

    A) \[A\ne O\]

    B) \[A=O\]

    C) \[A=I\]

    D) None of these

    Correct Answer: B

    Solution :

    Since \[|B|\ne 0\Rightarrow {{B}^{-1}}\]exists, \ \[AB=0\] Þ \[(AB){{B}^{-1}}=O{{B}^{-1}}\Rightarrow \,\,A(B{{B}^{-1}})=O\] Þ \[AI=O\Rightarrow A=O\].


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