Home
Class 12
MATHS
If AB+BA=0, then which of the following ...

If `AB+BA=0`, then which of the following is equivalent to `A^(3)-B^(3)`

A

A. `(A-B)(A^(2)+AB+B^(2))`

B

B. `(A-B)(A^(2)-AB-B^(2))`

C

C. `(A+B)(A^(2)-AB-B^(2))`

D

D. `(A+B)(A^(2)+AB-B^(2))`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `(A+B)(A^(2)-AB-B^(2))=A^(3)-A^(2)B-AB^(2)+BA^(2)-BAB-B^(3)`
`=A^(3)-B^(3)-A^(2)B-AB^(2)-ABA+AB^(2)` ( `:' AB=-BA`)
`=A^(3)-B^(3)-A^(2)B+A^(2)B`
`=A^(3)-B^(3)`
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 ne 0 and B ne 0 are two 2xx2 matrices such that AB = 0, then which of the following is correct ?

If A and B are two square matrices of order 3xx3 which satify AB=A and BA=B , then Which of the following is true ?

If the matrix A and B are of 3xx3 and (I-AB) is invertible, then which of the following statement is/are correct ?

Solve the following inequalities : (abs(x-1)-3)(abs(x+2)-5)lt0

a^(3)-b^(3)+1+3ab

A and B arer two matrices of order 3xx3 which satisfy AB = A and BA = B. Which of the following are true?

prove that |{:(a,b,0),(0,a,b),(b,0,a):}|=a^3+b^3 , hence , find the value of the following determinant : |{:(2ab,a^2,b^2),(a^2,b^2,2ab),(b^2,2ab,a^2):}|

Let's find the product of the following:- 2a^2b, 3ab^2

Let A=[(2,4),(3,2)], B=[(1,3),(-2,5)], C=[(-2,5),(3,4)] Find each of the following: (i) A+B (ii) A-B (iii) 3A-C (iv) AB (v) BA

If a - b = - 1 then find the value of (a^(3)-b^(3)+3ab+1)

CENGAGE PUBLICATION-MATRICES-All Questions
  1. If A=[a(ij)](mxxn) and a(ij)=(i^(2)+j^(2)-ij)(j-i), n odd, then which ...

    Text Solution

    |

  2. If det, (A-B) ne 0, A^(4)=B^(4), C^(3) A=C^(3)B and B^(3)A=A^(3)B, the...

    Text Solution

    |

  3. If AB+BA=0, then which of the following is equivalent to A^(3)-B^(3)

    Text Solution

    |

  4. A,B,C are three matrices of the same order such that any two are symme...

    Text Solution

    |

  5. If A and P are different matrices of order n satisfying A^(3)=P^(3) an...

    Text Solution

    |

  6. Let A, B are square matrices of same order satisfying AB=A and BA=B th...

    Text Solution

    |

  7. The number of 2xx2 matrices A, that are there with the elements as rea...

    Text Solution

    |

  8. If the orthogonal square matrices A and B of same size satisfy detA+de...

    Text Solution

    |

  9. If A=[[cos theta , sin theta],[sin theta,-costheta]], B = [[1,0],[-1,1...

    Text Solution

    |

  10. Let A be a 3xx3 matrix given by A=(a(ij))(3xx3). If for every column v...

    Text Solution

    |

  11. Let A and B be two non-singular matrices such that A ne I, B^(3) = I...

    Text Solution

    |

  12. Let A be a 2xx3 matrix, whereas B be a 3xx2 amtrix. If det.(AB)=4, the...

    Text Solution

    |

  13. Let A be a square matrix of order 3 so that sum of elements of each ro...

    Text Solution

    |

  14. A and B be 3xx3 matrices such that AB+A+B=0, then

    Text Solution

    |

  15. If (A+B)^(2)=A^(2)+B^(2) and |A| ne 0 , then |B|= (where A and B are m...

    Text Solution

    |

  16. If A=[{:(1,0,0),(1,0,1),(0,1,0):}], then which is true (a) A^(3)-A^(2...

    Text Solution

    |

  17. If the elements of a matrix A are real positive and distinct such that...

    Text Solution

    |

  18. If A=[{:(8,-6,2),(-6,7,-4),(2,-4,3):}] and X is a non zero column matr...

    Text Solution

    |

  19. If A, B are two square matrices of same order such that A+B=AB and I i...

    Text Solution

    |

  20. If A is a square matrix of order 3 such that |A|=5, then |Adj(4A)|=

    Text Solution

    |