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

  • question_answer
    Let \[A={{[{{a}_{ij}}]}_{m\times m}}\] be a matrix and \[C={{[{{c}_{ij}}]}_{m\times m}}\] be another matrix where \[{{c}_{ij}}\] is the cofactor of \[{{a}_{ij}}\]Then, what is the value of \[|AC|\]?

    A) \[|A{{|}^{m-1}}\]

    B) \[|A{{|}^{m}}\]

    C) \[|A{{|}^{m+1}}\]

    D) Zero

    Correct Answer: C

    Solution :

    [c] Let \[A={{[{{a}_{ij}}]}_{m\times m}}\] be a matrix and \[C={{[{{c}_{ij}}]}_{m\times m}}\] be another matrix where \[{{c}_{ij}}\] is the cofactor of \[{{a}_{ij}}\] \[\therefore \]      The value of \[\left| AC \right|={{\left| A \right|}^{m+1}}\]


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