Home
Class 12
MATHS
Let A ,\ B be two matrices such that ...

Let `A ,\ B` be two matrices such that they commute. Show that for any positive integer `n` , `A B^n=B^n A`

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

Let A ,\ B be two matrices such that they commute. Show that for any positive integer n , (A B)^n=A^n B^n

Let A ,B be two matrices such that they commute. Show that for any positive integer n , (i) A B^n=B^n A (ii) (A B)^n=A^nB^n

Let A ,B be two matrices such that they commute, then for any positive integer n , (i) A B^n=B^n A (ii) (A B)^n =A^n B^n

Let A and B are two matrices such that AB = BA, then for every n in N

If A is a square matrix such that |A| = 2 , then for any positive integer n, |A^(n)| is equal to

If Aa n dB are square matrices of the same order and A is non-singular, then for a positive integer n ,(A^(-1)B A)^n is equal to A^(-n)B^n A^n b. A^n B^n A^(-n) c. A^(-1)B^n A^ d. n(A^(-1)B^A)^

If A and B are two matrices such that rank of A = m and rank of B = n, then

If B ,C are square matrices of order na n difA=B+C ,B C=C B ,C^2=O , then without using mathematical induction, show that for any positive integer p ,A^(p+1)=B^p[B+(p+1)C] .

If B ,C are square matrices of order na n difA=B+C ,B C=C B ,C^2=O , then without using mathematical induction, show that for any positive integer p ,A^(p+1)=B^p[B+(p+1)C] .

If A a n d B are two non-singular matrices of the same order such that B^r=I , for some positive integer r >1,t h e n (A^(-1)B^(r-1)A)-(A^(-1)B^(-1)A)= a. I b. 2I c. O d. -I

RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. Let A=[2 3-1 2] and f(x)=x^2-4x+7 . Show that f(A)=O . Use this result...

    Text Solution

    |

  2. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. Show that A B!=B A in the following case: A=[5-1 6 7] and B=[2 1 3 ...

    Text Solution

    |

  10. Compute the products A B and B A whichever exists in each of the fol...

    Text Solution

    |

  11. Compute the products A B and B A whichever exists in each of the fol...

    Text Solution

    |

  12. Show that A B!=B A in each of the following cases: A=[[1, 3,-1],[2,-...

    Text Solution

    |

  13. Evaluate the following: ([(1,3),( -1,-4))]+[(3 ,-2 ),(-1 ,1)])[(1 ,3,5...

    Text Solution

    |

  14. If A=[[1, 0],[ 0, 1]] , B=[[1,0],[0,-1]] and C=[[0, 1],[ 1, 0]] , then...

    Text Solution

    |

  15. If A=[[2,-1],[ 3, 2]] and B=[[0, 4],[-1, 7]] , find 3A^2-2B+I .

    Text Solution

    |

  16. If A=[[4, 2],[-1, 1]] , prove that (A-2I)(A-3I)=O .

    Text Solution

    |

  17. If A=[(1,1),(0,1)] , show that A^2=[(1, 2),( 0, 1)] and A^3=[(1 ,3 ),(...

    Text Solution

    |

  18. If A=[(ab ,b^2) ,(-a^2 ,-ab)] , show that A^2=O .

    Text Solution

    |

  19. If A=[cos2thetasin2theta-sin2thetacos2theta] , find A^2 .

    Text Solution

    |

  20. If A=[(2 ,-3, -5), (-1, 4, 5),( 1, -3 ,-4)] and B=[(-1, 3, 5), (1,-3, ...

    Text Solution

    |