Home
Class 12
MATHS
If A, B are square materices of same ord...

If A, B are square materices of same order and B is a skewsymmetric matrix, show that `A^(T)BA` is skew-symmetric.

Text Solution

Verified by Experts

Matric B is skew-symmetric
`:. B^(T)=-B`
Now, `(A^(T)BA)^(T)=A^(T)B^(T) (A^(T))^(T)" "("as "(AB)^(T)=B^(T)A^(T))`
`=A^(T)(-B)A`
`=-A^(T) BA`
Hence, `A^(T)BA` is a skew-symmetric matrix.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • MATHMETICAL REASONING

    CENGAGE PUBLICATION|Exercise Archives|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|7 Videos

Similar Questions

Explore conceptually related problems

If A, B are symmetric matrices of same order, then AB-BA is a

If A and B are symmetric matrices, prove that AB-BA is a skew symmetric matrix.

Knowledge Check

  • If A and B are two square matrices of the same order, then (A-B)^(2) is equal to -

    A
    `A^(2)-2AB+B^(2)`
    B
    `A^(2)-AB-BA+B^(2)`
    C
    `A^(2)-2BA+B^(2)`
    D
    `A^(2)+2AB+B^(2)`

  • If A and B are square matrices of the same order such that AB = A and BA = B, then……

    A
    `A^(2)=A`
    B
    `B^(2)=B`
    C
    `A=I`
    D
    `B=I`

    • Similar Questions

    Explore conceptually related problems

    If A and B are square matrices of the same order, then AB = 0 implies

    Prove that inverse of a skew-symmetric matrix (if it exists) is skew-symmetric.

    A,B,C are three matrices of the same order such that any two are symmetric and the 3^(rd) one is skew symmetric. If X=ABC+CBA and Y=ABC-CBA , then (XY)^(T) is

    If A and B are matrices of the same order, then A B^T-B A^T is a (a) skew-symmetric matrix (b) null matrix (c) unit matrix (d) symmetric matrix

    Let A be a square matrix. Then prove that (i) A + A^T is a symmetric matrix and, (ii) A -A^T is a skew-symmetric matrix

    If A and B are square matrices of same order such that AB=O and B ne O , then prove that |A|=0 .

    Home
    Profile