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

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

Promotional Banner

Topper's Solved these Questions

  • LINEAR PROGRAMMING

    V PUBLICATION|Exercise QUESTION BANK|39 Videos

  • PROBABILITY

    V PUBLICATION|Exercise QUESTION BANK|132 Videos

Similar Questions

Explore conceptually related problems

If A and B are symmetric matrices of the same order, then prove that (A+B) is also symmetric.

Let A and B be two symmetric matrices of same order. Then show that AB-BA is a skew-symmetric matrix.

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

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

Suppose A and B are two symmetric matrices. If AB is symmetric, prove that AB =BA

Suppose A and B are two symmetric matrices. Prove that (AB)^T = BA

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

If A and B are square matrices of the same order such that A B=B A ,then prove by induction that AB^n=B^n A . Further, prove that (AB)^n = A^n B^n for all n in N .

If A and B are symmetric matrices of the same order the X = AB + BA and Y = AB-BA, then XY^(T) is equal to a)XY b)YX c) -YX d)None of these

If A and B are matrices of order 3 such that abs[A]=-1 , abs[B]=3 ,then abs[3AB] is

V PUBLICATION-MATRICES-QUESTION BANK
  1. Find the inverse of the following matrices if it exists.[[2, 1],[ 4,...

    Text Solution

    |

  2. If A=[[cos theta, sin theta],[ -sin theta, cos theta]], then prove ...

    Text Solution

    |

  3. If A and B are symmetric matrices of the same order, then show that A ...

    Text Solution

    |

  4. Let A=[[2 , -1],[3 , 4]], B=[[5, 2],[ 7, 4]] , C=[[2, 5],[ 3, 8]...

    Text Solution

    |

  5. If A=[[1 , 1, 1],[ 1, 1, 1],[ 1, 1 , 1]], prove that A^n=[[3^(n-...

    Text Solution

    |

  6. if A=[[3, -4],[ 1, (-1)]], then prove that A^n=[[1+2 n, -4 n ],[n...

    Text Solution

    |

  7. If A and B are symmetric matrices, prove that A B-B A is a skew symmet...

    Text Solution

    |

  8. Show that the matrix B^' A B is symmetric or skew symmetric according ...

    Text Solution

    |

  9. Find the values of x, y, z, if the matrix A=[[0, 2 y, z],[ x, y, ...

    Text Solution

    |

  10. For what values of x:[[1, 2, 1]] [[1, 2, 0],[ 2, 0, 1],[ 1, 0...

    Text Solution

    |

  11. If A=[[3,1],[-1,2]] then Hence show that A^2-5A+7I=0

    Text Solution

    |

  12. Find x, if [[x,-5,-1]] [[1, 0, 2],[ 0, 2, 1],[ 2, 0, 3]][[x],[...

    Text Solution

    |

  13. Find the matrix X so that X[[1 , 2, 3],[ 4, 5, 6]]=[[-7, -8, -9]...

    Text Solution

    |

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

    Text Solution

    |

  15. If A=[[alpha ,beta],[ gamma , -alpha]] is such that A^2=I, then A) ...

    Text Solution

    |

  16. If the matrix A is both symmetric and skew symmetric, then: A)A is a d...

    Text Solution

    |

  17. If A is a square matrix such that A^2=A, then (I+A)^3-7 A is equal to ...

    Text Solution

    |

  18. Construct a m xx n matrix A=[[a(ij)]] whose elements a(ij) is given by...

    Text Solution

    |

  19. If [[a+b ,2],[ 5 , a b]]=[[6 , 2],[ 5, 8]], find the values of a an...

    Text Solution

    |

  20. Complete the following product [[1 , 0 , -5],[ 2, 0, 4]][[3 , 1],[ ...

    Text Solution

    |