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determinant OF matrix || adjoint OF matrix

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Knowledge Check

  • If A is matrix of order 3 such that |A|=5 and B= adj A, then the value of ||A^(-1)|(AB)^(T)| is equal to (where |A| denotes determinant of matrix A. A^(T) denotes transpose of matrix A, A^(-1) denotes inverse of matrix A. adj A denotes adjoint of matrix A)

    A
    5
    B
    1
    C
    25
    D
    `(1)/(25)`
  • If A and B are non - singular matrices of order 3xx3 , such that A=(adjB) and B=(adjA) , then det (A)+det(B) is equal to (where det(M) represents the determinant of matrix M and adj M represents the adjoint matrix of matrix M)

    A
    1
    B
    2
    C
    3
    D
    4
  • Let B is an invertible square matrix and B is the adjoint of matrix A such that AB=B^(T) . Then

    A
    A is an identity matrix
    B
    B is symmetric matrix
    C
    A is a skew-symmetric matrix
    D
    B is skew symmetic matrix
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