Home
Class 12
MATHS
If A and B are square matrices of ord...

If `A` and `B` are square matrices of order `n` , then prove that `A` and `B` will commute iff `A-lambda\ I` and `B-lambda\ I` commute for every scalar `lambda`

Promotional Banner

Topper's Solved these Questions

  • ADJOINTS AND INVERSE OF MATRIX

    RD SHARMA ENGLISH|Exercise All Questions|181 Videos

  • ALGEBRA OF VECTORS

    RD SHARMA ENGLISH|Exercise All Questions|325 Videos

Similar Questions

Explore conceptually related problems

If A and B are square matrices of order n , then prove that A \ a n d \ B will commute iff A-lambdaI \ a n d \ B-lambdaI commute for every scalar lambda .

If A and B are square matrices of order n , then prove that Aa n dB will commute iff A-lambdaIa n dB-lambdaI commute for every scalar lambdadot

If A and B are square matrices of order n , then prove that Aa n dB will commute iff A-lambdaIa n dB-lambdaI commute for every scalar lambdadot

If A and B are square matrices of the same order such that |A|=3 and A B=I , then write the value of |B| .

If A and B are commuting square matrices of the same order, then which of the following is/are correct ?

If A and B are two square matrices such that they commute, then which of the following is true?

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 A B = B A .

If A and B matrices commute then

If A and B are symmetric matrices, then show that A B is symmetric if A B=B A i.e. A and B commute.

If A is a square matrix of order nxxn such that |A|=lambda , then write the value of |-A| .

RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. If A is any mxxn such that A B and B A are both defined show that B...

    Text Solution

    |

  2. A ,\ B are two matrices such that A B and A+B are both defined; sho...

    Text Solution

    |

  3. If A and B are square matrices of order n , then prove that A and B...

    Text Solution

    |

  4. If A B=A and B A=B , then show that A^2=A , B^2=B .

    Text Solution

    |

  5. Give an example of two matrices A and B such that A!=O ,\ \ B!=O ,\ ...

    Text Solution

    |

  6. Give an example of three matrices A ,\ B ,\ C such that A B=A C but...

    Text Solution

    |

  7. There are 2 families A and B. There are 4 men, 6 women and 2 children ...

    Text Solution

    |

  8. Use matrix multiplication to divide Rs. 30,000 in two parts such that ...

    Text Solution

    |

  9. Three schools A ,\ B and C organised a mela for collecting funds fo...

    Text Solution

    |

  10. Prove that the product of matrices [cos^2thetacosthetasinthetacosthe...

    Text Solution

    |

  11. Let A=[(0,-tan(alpha/2)),(tan(alpha/2),0)] and I be the identity matr...

    Text Solution

    |

  12. Let F(x)=[cosx -sinx 0 sinx cosx 0 ...

    Text Solution

    |

  13. Let A=[2 3-1 2] and f(x)=x^2-4x+7 . Show that f(A)=O . Use this result...

    Text Solution

    |

  14. If A=[0 1 0 0] , prove that (a I+b A)^n=a^n\ I+n a^(n-1)\ b A where I ...

    Text Solution

    |

  15. Let A ,\ B be two matrices such that they commute. Show that for an...

    Text Solution

    |

  16. Let A ,\ B be two matrices such that they commute. Show that for an...

    Text Solution

    |

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

    Text Solution

    |

  18. If A is a square matrix such that A^2=I , then find the simplified...

    Text Solution

    |

  19. If A=[3\ \ \ 5] , B=[7\ \ \ 3] , then find a non-zero matrix C such...

    Text Solution

    |

  20. Compute the indicated products: [a b-b a][a-bb a] (ii) [1-2 2 3][1 ...

    Text Solution

    |