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

  • question_answer
    Let A be an \[n\times n\] matrix. If \[\det \,(\lambda A)={{\lambda }^{s}}\det \,(A),\] what is the value of s?

    A) \[0\]

    B) \[1\]

    C) \[-1\]

    D) \[n\]

    Correct Answer: D

    Solution :

    [d] We know, if A is an \[n\times n\] matrix, then \[\det (\lambda A)={{\lambda }^{s}}\det (A)\] But given \[\det (\lambda A)={{\lambda }^{s}}\det \,A\Rightarrow s=n\]


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