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

  • question_answer
    If A and B be two square matrices of order \[\lambda \]whose all the elements are essentially positive integers then the minimum value of \[tr\text{ (}A{{B}^{2}})\] is equal to                    

    A) \[{{\lambda }^{3}}\]

    B) \[{{\lambda }^{2}}\]

    C) \[2{{\lambda }^{2}}\]

    D) None of these

    Correct Answer: B

    Solution :

    [b] \[tr(A)=\sum\limits_{i=1}^{\lambda }{{{a}_{ii}}\ge \lambda (As\,\,{{a}_{ij}}\ge 1i,\,j)}\] and \[tr(M{{N}^{2}})=\{tr(M)\}{{\{tr(N)\}}^{2}}\]


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