Home
Class 12
MATHS
Sum of two skew-symmetric matrices is al...

Sum of two skew-symmetric matrices is always ......... Matrix.

Text Solution

Verified by Experts

Let A is a given matrix, then (-A) is a skew symmetric matrix Similarly, for a given matrix -B is a skew -symmetric matrix.
Hence -A-B=-(A+B)`rArr` sum of two skew symmetric matrices is always skew symmetric m atrix.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • LINEAR PROGRAMMING

    NCERT EXEMPLAR|Exercise Linear Programming|45 Videos

  • PROBABILITY

    NCERT EXEMPLAR|Exercise Probability|107 Videos

Similar Questions

Explore conceptually related problems

If A is a skew-symmetric matrix, then A^(2) is a .................

If A is skew-symmetric matrix then A^(2) is a symmetric matrix.

Knowledge Check

  • Trace of a skew symmetric matrix is always equal to

    A
    `sum a_(ij)`
    B
    ` sum a_(ii)`
    C
    zero
    D
    none of these

  • 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

  • If A and B are two skew symmetric matrices of order n then

    A
    AB is a skew symmetric matrix
    B
    AB is a symmetric matrix
    C
    AB is a symetric matrix if A and B commute
    D
    none of these

    • Similar Questions

    Explore conceptually related problems

    Symmetric & Skew metric matrix

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

    If A and B are symmetric matrices,then ABA is (a) symmetric matric b) skew-symmetric matrix (c) diagonal matrix (d) scalar matrix

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

    If A is skew-symmetric matrix, then trace of A is

    Home
    Profile