Home
Class 12
MATHS
If A and B are symmetric matrices of sam...

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

Text Solution

Verified by Experts

If A and B are symmetric matrices of same order, then Ab is symmetric if and only is AB=BA.
`therefore (AB)'`
=B'A'=BA
=AB `[because AB=BA]`
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,B are symmetric matrices of same order, then AB-BA is a :

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

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

If A and B are symmetric matrices of the same order,then show that AB is symmetric if and only if A and B commute,that is AB=BA

If A and B are symmetric matrices of the same order, show that AB+BA is symmetric.

If A and B are symmetric matrices of the same order then (AB-BA) is always

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

If A and B are symmetric matrices,then ABA is

NCERT EXEMPLAR-MATRICES-Matrices
  1. If A and B are symmetric matrices, then (i) AB-BA is a .......... ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. In applying one or more row operations while finding A^(-1) by elemen...

    Text Solution

    |

  5. A matrix denotes a number

    Text Solution

    |

  6. Matrices of any order can be added.

    Text Solution

    |

  7. Two matrices are equal. If they have same number of rows and same numb...

    Text Solution

    |

  8. Matrices of different order cannot be subtracted.

    Text Solution

    |

  9. Matrix addition is associative as well as commutative.

    Text Solution

    |

  10. Matrix m ultiplication is commutative.

    Text Solution

    |

  11. A square m atrix where every element is unity is called an identity ma...

    Text Solution

    |

  12. If A and B are two square matrices of the same order, then A+B=B+A.

    Text Solution

    |

  13. If A and B are two m atrices of the same order, then A-B=B-A.

    Text Solution

    |

  14. If A dn B be 3xx3 matrices the AB=0 implies (A) A=0 or B=0 (B) A=0 and...

    Text Solution

    |

  15. Transpose of a column matrix is a column matrix.

    Text Solution

    |

  16. If A and B are square matrices of the same order such that A B=B A , t...

    Text Solution

    |

  17. If each of the three matrices of the same order are symmetric, then th...

    Text Solution

    |

  18. If A and B are any two matrices of the same order, then (AB)=A'B'

    Text Solution

    |

  19. If (AB)'=B'A', where A and B are not square matrices, then number of r...

    Text Solution

    |

  20. Let A; B; C be square matrices of the same order n. If A is a non sing...

    Text Solution

    |