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The determinant of a skew symmetric mat...

The determinant of a skew symmetric matrix of odd order is
0
1
- 1
None of these

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Statement 1: The determinant of a matrix A=[a_(ij)]_(5xx5) where a_(ij)+a_(ji)=0 for all i and j is zero.Statement 2: The determinant of a skew-symmetric matrix of odd order is zero

The trace of a skew symmetric matrix of odd order is equal to its A.Determinant value C. Order B.Transpose D.Index

Knowledge Check

  • Consider the matrix A=[{:(0,-h,-g),(h,0,-f),(g,f, 0):}] STATEMENT-1 : Det A = 0 STATEMENT-2 :The value of the determinant of a skew symmetric matrix of odd order is always zero.

    A
    Statement - 1 is True, Statement - 2 is True' Statement - 2 is a correct explanation for Statement - 1
    B
    Statement - 1 is True, Statement - 2 is True, Statement - 2 is Not a correct explanation for Statement - 1
    C
    Statement - 1 is True, Statement - 2 is False
    D
    Statement - 1 is False, Statement - 2 is True

  • The inverse of a skew symmetric matrix is

    A
    a symmetric matrix if it exists
    B
    a skew symmetric matrix if it exists
    C
    transpose of the original matrix
    D
    may not exist

  • 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

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    If A is a skew-symmetric matrix of odd order n, then |A|=O .

    If A is a skew-symmetric matrix of odd order n, then |A|=0

    The inverse of a skew symmetric matrix of odd order is 1)a symmetric matrix 2)a skew symmetric matrix 3)a diagonal matrix 4)does not exist

    Show that every skew-symmetric matrix of odd order is singular.

    If A be a skew symmetric matrix of odd order, then |A| is equal to

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