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Determinant of matrix order >=4...

Determinant of matrix order >=4

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Introduction |Order of determinant|Determinant of Matrix |Properties of Determinant |Previous year questions |Area of a Triangle

Introduction |Order of determinant|Determinant of Matrix |Properties of Determinant |Previous year questions |Area of a Triangle

Knowledge Check

  • Statement -1 : Determinant of a skew-symmetric matrix of order 3 is zero. Statement -2 : For any matrix A, Det (A) = "Det"(A^(T)) and "Det" (-A) = - "Det" (A) where Det (B) denotes the determinant of matrix B. Then,

    A
    Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 6
    B
    Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 6
    C
    Statement 1 is true, Statement 2 is False
    D
    Statement 1 is False, Statement 2 is true

  • 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)`

  • Let the determinant of a 3xx3 matrix A be 6, then B is a matrix defined by B=5A^(2) . Then, determinant of B is

    A
    180
    B
    100
    C
    80
    D
    none of these

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    Let A be a square matrix of order 2 such that A-1 = AA^(T) (where I is an identity matrix of order 2), then which one of the following is INCORRECT statement (where |A| represents determinant value of matrix A)

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