Home
Class 12
MATHS
If det, (A-B) ne 0, A^(4)=B^(4), C^(3) A...

If det, `(A-B) ne 0, A^(4)=B^(4), C^(3) A=C^(3)B` and `B^(3)A=A^(3)B`, then find the value of det. `(A^(3)+B^(3)+C^(3))`.

A

`0`

B

`1`

C

`3|A|^(3)`

D

`6`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` `(A^(3)+B^(3)+C^(3))(A-B)=A^(4)-A^(3)B+B^(3)A-B^(4)+C^(3)A-C^(3)B=0`
`implies|(A^(3)+B^(3)+C^(3))(A-B)|=0`
`implies|(A^(3)+B^(3)+C^(3))|=0`, since `|(A-B)|ne0`
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

A and B are different matrices of order n satisfying A^(3)=B^(3) and A^(2)B=B^(2)A . If det. (A-B) ne 0 , then find the value of det. (A^(2)+B^(2)) .

If a+b+c=10,a^(2)+b^(2)+c^(2)=38 and a^(3)+b^(3)+c^(3)=160 then find the value of 3abc.

a+b+c=6,a^(2)+b^(2)+c^(2)=14 and a^(3)+b^(3)+c^(3)=36 then find the value of 3abc.

If a = b = c = 99999 , then find the value of (a^(3)+b^(3)+c^(3)-3abc)

If a/2=b/3 =c/4 =(3a-ab+4c)/p , then find the value of p.

If a+b+c=9,a^(2)+b^(2)+c^(2)=27 and a^(3)+b^(3)+c^(3)=81 then find the value of 3abc.

If a=3, b=4, c=5, find the value of tan( B/2) .

If P(A) = 2/3, P(B) = 1/2 and P(A uu B) = 3/4 then find the value of P(A^C uu B^C) .

If a/2=b/3=c/5=(3a-5b+4c)/(K) then find the value of K.

Consider, A=[(a,2,1),(0,b,0),(0,-3,c)] , where a, b and c are the roots of the equation x^(3)-3x^(2)+2x-1=0 . If matric B is such that AB=BA, A+B-2I ne O and A^(2)-B^(2)=4I-4B , then find the value of det. (B)

CENGAGE PUBLICATION-MATRICES-All Questions
  1. A=[{:(a,b),(b,-a):}] and MA=A^(2m), m in N for some matrix M, then whi...

    Text Solution

    |

  2. If A=[a(ij)](mxxn) and a(ij)=(i^(2)+j^(2)-ij)(j-i), n odd, then which ...

    Text Solution

    |

  3. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |