JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Special types of matrices, Transpose, Adjoint and Inverse of matrices

  • question_answer
    If X is a square matrix of order 3 × 3 and \[\lambda \] is a scalar, then adj (\[\lambda X)\] is equal to [J & K 2005]

    A) \[\lambda \,adjX\]

    B) \[{{\lambda }^{3}}adj\,X\]

    C) \[{{\lambda }^{2}}adj\,X\]

    D) \[{{\lambda }^{4}}adj\,X\]

    Correct Answer: C

    Solution :

    By fundamental property, \[adj(\lambda X)={{\lambda }^{n-1}}(adj\,X)\]. Here \[n=3\] \\[adj(\lambda X)={{\lambda }^{3-1}}(adj\,X)\]    \[adj(\lambda X)={{\lambda }^{2}}(adj\,X)\].


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