JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Self Evaluation Test - Determinats

  • question_answer
    Let A and B be two matrices of order\[n\times n\]. Let A be non-singular and B be singular. Consider the following:
    1. AB is singular
    2. AB is non-singular
    3. \[{{A}^{-1}}B\] is singular
    4.\[{{A}^{-1}}B\] is non singular
    Which of the above is/ are correct?

    A) 1 and 3

    B) 2 and 4 only

    C) 1 only

    D) 3 only

    Correct Answer: B

    Solution :

    [b] If A is non-singular and B is singular, then AB and \[{{A}^{-1}}B\] are non-singular. Statements (2) and (4) are correct.


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