Home
Class 12
MATHS
If Aa n dB are two matrices such that A ...

If `Aa n dB` are two matrices such that `A B=Ba n dB A=A ,t h e n` `(A^5-B^5)^3=A-B` b. `(A^5-B^5)^3=A^3-B^3` c. `A-B` is idempotent d. none of these

Promotional Banner

Topper's Solved these Questions

  • MATHMETICAL REASONING

    CENGAGE PUBLICATION|Exercise Archives|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|7 Videos

Similar Questions

Explore conceptually related problems

if A and B are two matrices of order 3xx3 so that AB=A and BA=B then (A+B)^7=

If A and B are square matrices such that AB = BA then prove that A^(3)-B^(3)=(A-B) (A^(2)+AB+B^(2)) .

If Aa n dB are two independent events such that P(A)=1//2 a n d P(B)=1//5, then

If Aa n dB are two events such that P(A)=1/2a n dP(B)=2/3 . Then show that P(A U B) ge 2/3 .

If A and B are two square matrices such that B=-A^(-1)B A ,t h e n(A+B)^2 is equal to a. A^2+B^2 b. O c. A^2+2A B+B^2 d. A+B

If A and B are two non-singular matrices such that A B=C ,t h e n,|B| is equal to a. (|C|)/(|A|) b. (|A|)/(|C|) c. |C| d. none of these

A and B arer two matrices of order 3 × 3 which satisfy AB = A and BA =B then (A+B)^(7) is equal to___

If A B=Aa n dB A=B , then a. A^2B=A^2 b. B^2A=B^2 c. A B A=A d. B A B=B

If A and B are two square matrices of order 3xx3 which satify AB=A and BA=B , then (A+I)^(5) is equal to (where I is idensity matric)

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

CENGAGE PUBLICATION-MATRICES-All Questions
  1. If P is an orthogonal matrix and Q=P A P^T an dx=P^T Q^1000 P then x^...

    Text Solution

    |

  2. If A is a nilpotent matrix of index 2, then for any positive integer n...

    Text Solution

    |

  3. If Aa n dB are two matrices such that A B=Ba n dB A=A ,t h e n (A^5-B...

    Text Solution

    |

  4. If Z is an idempotent matrix, then (I+Z)^n I+2^n Z b. I+(2^n-1)Z c. ...

    Text Solution

    |

  5. If A is an orthogonal matrix then A^(-1) equals a.A^T b. A c. A^2 ...

    Text Solution

    |

  6. If A^2=I, then the value of det(A-I) is (where A has order 3) 1 b. -1 ...

    Text Solution

    |

  7. Let A be an nth-order square matrix and B be its adjoint, then |A B+K ...

    Text Solution

    |

  8. A=[(a,1,0),(1,b,d),(1,b,c)],B=[(a,1,1),(0,d,c),(f,g,h)],U=[(f),(g),(h)...

    Text Solution

    |

  9. If M is a 3 xx 3 matrix, where det M=1 and MM^T=1, where I is an ident...

    Text Solution

    |

  10. If A is a diagonal matrix of order 3xx3 is commutative with every squa...

    Text Solution

    |

  11. Let S be the set which contains all possible values of l ,m ,n ,p ,q ,...

    Text Solution

    |

  12. Given a matrix A=[(a,b,c),(b,c,a),(c,a,b)], where a, b, c are real pos...

    Text Solution

    |

  13. If A is a square matrix of order 3 such that |A|=2,t h e n|(a d jA^(-1...

    Text Solution

    |

  14. Let A=[[3x^2], [1], [6x]],B=[a,b,c]and C=[[(x+2)^2, 5x^2, 2x],[5x^2, 2...

    Text Solution

    |

  15. If A is an idempotent matrix satisfying, (I-0. 4 A)^(-1)=I-alphaA ,w h...

    Text Solution

    |

  16. Let A=([a(i j)])(3xx3) be a matrix such that AA^T=4Ia n da(i j)+2c(i j...

    Text Solution

    |

  17. Let A be the set of all 3xx3 skew-symmetri matrices whose entries are ...

    Text Solution

    |

  18. If A=[[0, 1,2],[1,2,3],[3,a,1]]and A^(-1)[[1//2,-1//2,1//2],[-4,3,b],[...

    Text Solution

    |

  19. For two unimodular complex number z1a n dz2 [[barz1, -z2], [barz2, z1...

    Text Solution

    |

  20. If Aa n dB are two non-singular matrices of the same order such that B...

    Text Solution

    |