Home
Class 12
MATHS
if A and B are matrices of same order, t...

if A and B are matrices of same order, then `(AB'-BA')` is a 1) null matrix 3)symmetric matrix 2) skew -symmetric matrix 4)unit matrix

A

skew-symmetric matrix

B

null matrix

C

symmetric matrix

D

unit matrix

Text Solution

Verified by Experts

We have matrices A and B of same order.
Let `P=(AB'-BA')`
Then, `P'=(AB'-BA')'=(AB)'=(BA)'`
=(B)(A)-(A)B=BA-AB
`=-(AB-BA)=-P`
Hence (AB-BA) is a skew-symmetric matrix.
Promotional Banner

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 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 and B are symmetric of the same order, then (A) AB is a symmetric matrix (B) A-B is skew symmetric (C) AB-BA is symmetric matrix (D) AB+BA is a symmetric matrix

Choose the correct answer If A,B are symmetric matrices of same order,then AB BA is a (A) Skew symmetric matrix (B) Symmetric matrix (C) Zero matrix (D) Identity matrix

Orthogonal Matrix ||Symmetric Matrix || Skew Symmetric Matrix

Let A and B be symmetric matrices of same order. Then A+B is a symmetric matrix, AB-BA is a skew symmetric matrix and AB+BA is a symmetric matrix

A square matrix A is said skew - symmetric matrix if

If A and B are two symmetric matrix of same order,then show that (AB-BA) is skew symmetric matrix.

If AB are symmetric matrices of same order then show that AB-BA is a skew symmetric matrix.

If A and B are symmetrices matrices of the same order, then A B^T B A^T is a (a) skew-symmetric matrix (b) null matrix (c) symmetric matrix (d) none of these

NCERT EXEMPLAR-MATRICES-Matrices
  1. The matrix [{:(0,-5,8),(5,0,12),(-8,-12,0):}] is a

    Text Solution

    |

  2. If A is matrix of order mxxn and B is a matrix such that AB' and B'A ...

    Text Solution

    |

  3. if A and B are matrices of same order, then (AB'-BA') is a 1) null mat...

    Text Solution

    |

  4. If A is a square matrix such that A^(2)= I, then (A-I)^(3)+(A+I)^(3)...

    Text Solution

    |

  5. For any two matrices A and B , we have

    Text Solution

    |

  6. On usign elementry column operation C(2)rArrC(2)-2C(1) in the followin...

    Text Solution

    |

  7. On using row operation R(1)rArrR(1)-3R(2) in the following matrix equa...

    Text Solution

    |

  8. ......... Matrix is both symmetric and skew-symmetric matrix.

    Text Solution

    |

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

    Text Solution

    |

  10. The negative of a matrix is obtained b y multiplying it by ...........

    Text Solution

    |

  11. The product of any matrix by the scalar ......... Is the null matrix.

    Text Solution

    |

  12. A matrix which is not a square matrix is called a..........matrix.

    Text Solution

    |

  13. Matrix multiplication is distributive over matrix addition

    Text Solution

    |

  14. If A is a symmetric matrix , then A^(3) is a ........ Matrix.

    Text Solution

    |

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

    Text Solution

    |

  16. If A and B are square matrices of the same order, then (i) (AB)=.......

    Text Solution

    |

  17. If A is a skew-symmetric, then kA is a...........(where, k is any scal...

    Text Solution

    |

  18. If A and B are symmetric matrices, then (i) AB-BA is a .......... ...

    Text Solution

    |

  19. If A is symmetric matrix, then B'AB is............

    Text Solution

    |

  20. If A and B are symmetric matrices of same order, then AB is symmetric ...

    Text Solution

    |