Home
Class 11
MATHS
Statement -1 : Determinant of a skew-sym...

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

Text Solution

Verified by Experts

The correct Answer is:
C
Let A be a skew - symmetric matrix of order 3
Then,
`A^(T) = -A`
`rArr Det (A^(T)) = Det (-A)`
`rArr Det (A) = (-1)^(3) Det (A)`
`rArr Det(A) = - Det(A)`
`rArr 2Det(A) = 0`
`rArr Det (A) = 0`
So, statement -1 is true.
For any square matrix of order n, we have
`Det(A^(T)) = Det(A) and Det(-A) = (-1)^(n) Det(A)`
So, statement -2 is not true
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DETERMINANTS

    OBJECTIVE RD SHARMA|Exercise Exercise|94 Videos

  • DETERMINANTS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos

  • DETERMINANTS

    OBJECTIVE RD SHARMA|Exercise Section I - Solved Mcqs|74 Videos

  • CONIC SECTIONS

    OBJECTIVE RD SHARMA|Exercise Section I - Solved Mcqs|1 Videos

  • DISCRETE PROBABILITY DISTRIBUTIONS

    OBJECTIVE RD SHARMA|Exercise Exercise|40 Videos

Similar Questions

Explore conceptually related problems

If A is a skew-symmetric matrix of order 3, then prove that det A=0.

If matric A is skew-symmetric matric of odd order, then show that tr. A = det. A.

Knowledge Check

  • For a 3xx3 matrix A if det A=4, then det (Adj. A) equals

    A
    `-4`
    B
    `4`
    C
    `16`
    D
    `64`

    • Similar Questions

    Explore conceptually related problems

    If A is skew symmetric matrix of order 3 then det A is (A)0 (B)-A (C)A (D)none of these

    If A is a square matrix of order 3, then the true statement is (where I is unit matrix) (1)det(-A)=-det A(2) det A=0 (3) det(A+I)=1+det A(4)det(2A)=2det A

    If det(adjA)=|A|^(2), then the order of matrix A is

    Assertion (A): If A is skew symmetric matrix of order 3 then its determinant should be zero Reason (R): If A is square matrix then det(A)=det(A')=det(A')

    Let A be a square matreix of order n then det(A)=det(A^(T))

    If one of the eigenvalues of a square matrix a order 3xx3 is zero, then prove that det A=0 .

    If A is a square matrix of order 2 then det(-3A) is

    Home
    Profile