Home
Class 12
MATHS
If A and P are 3xx3 matrices with integr...

If A and P are `3xx3` matrices with integral entries such that P ' AP = A , then det . P is :

A

`-1`

B

1

C

always ±1

D

±1 provided `A ne 0`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL REASONING

    HIMALAYA PUBLICATION|Exercise Question Bank|97 Videos

  • MAXIMA AND MINIMA

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|167 Videos

Similar Questions

Explore conceptually related problems

If A and B are any 2xx2 matrices , then det (A+B) = 0 implies :

The number of 3xx3 non - singular matrices , with four entries as 1 and all other entries as 0 , is :

If A and P are the square matrices of the same order and if P be invertible, show that the matrices A and P^(-1) have the same characteristic roots.

If P is a 3xx3 matrix such that P^(T) = 2P +I, where P^(T) is the transpose f P and I is the 3xx3 identify matrix then there exists a column matrix X = [(x),(y),(z)] != [ (0),(0),(0)] such that :

If A and B are (-2, -2) and (2, -4), respectively, find the coordinates of P such that AP = (3)/(7)AB and P lies on the line segment AB.

If A,B and C are square matrices of order n and det (A)=2, det(B)=3 and det (C)=5, then find the value of 10det (A^(3)B^(2)C^(-1)).

If A and B are two events such that P(A)=(1)/(3), P(B)=(1)/(2) and P(AnnB)=(1)/(6) , then P(A'//B) is

Let P and Q be 3 xx3 matrices with P != Q . If P^(3) = Q^(3) and P^(2) Q = P^(2)Q = Q^(2) P , then determinant of (P^(2) + Q^(2)) is equal to :

Let M and N be two 3xx3 non - singular skew symmetric matrices such that MN = NM Let P^(T) denote the transpose of P , then : M^(2)N^(2) (M^(T)N)^(-1) (MN^(-1))^(T) is equal to :

If A and B are two events such that P(AcupB)=(5)/(6), P(A)=(1)/(3) and P(B)=(3)/(4) , then A and B are

HIMALAYA PUBLICATION-MATRICES AND DETERMINANTS-QUESTION BANK
  1. If [[ p , q-y , r-z],[ p-x , q , r-z ],[ p-x , q-y , r ]]=0, then (p)/...

    Text Solution

    |

  2. A and B are matrices of order three and |A| =4, |B| =-1 . Then the de...

    Text Solution

    |

  3. If A and P are 3xx3 matrices with integral entries such that P ' AP = ...

    Text Solution

    |

  4. Let A be a matrix of order 3 xx 3, and B is its adjoint matrix. If ...

    Text Solution

    |

  5. IF A is a 3 times 3 matrix, |A| ne 0 and |3A|=k|A|, then write the val...

    Text Solution

    |

  6. IF A is a 3 times 3 matrix, |A| ne 0 and |3A|=k|A|, then write the val...

    Text Solution

    |

  7. If alpha , beta and gammaare roots of the equations x^3+px+q=0 then th...

    Text Solution

    |

  8. Delta=|[x+a,b,c],[b,x+c, a],[c,a, x+b]| which of the following is a fa...

    Text Solution

    |

  9. The value of Delta= [[5^2 , 5^3 , 5^4],[ 5^3 , 5^4 , 5^5],[ 5^4 , 5^6 ...

    Text Solution

    |

  10. [[ 0 , p-q , p-r ],[q-p , 0 , q-r],[ r-p , r-q , 0 ]] =

    Text Solution

    |

  11. With the usual notation in the triangle A B C [[ 1 , 1 , 1 ],[ sin A...

    Text Solution

    |

  12. If A= [[-1 , 2 , 4 ],[ 3 , 1 , 0],[ -2 , 4 , 2 ]] and B= [[-2 , 4 ...

    Text Solution

    |

  13. If [[ a , b , c],[ m , n , p],[ x , y , z ]] =k, then [[ 6 a , 2 b ,...

    Text Solution

    |

  14. Delta= [[ 1 / a , 1 , b c ],[1 / b , 1 , c a ],[1 / c , 1 , a b]] =

    Text Solution

    |

  15. If [[ x , 2 , x],[x^2 , x , 6],[x , x , 6 ]] =a x^4+b x^3+c x^2+d x+e,...

    Text Solution

    |

  16. If omega is an imaginary cube root of unity then the value of [[1+ome...

    Text Solution

    |

  17. If alpha, beta, gamma are the roots of x^3+a x^2+b=0 then the value of...

    Text Solution

    |

  18. The area of a triangle with vertices (-3,0),(3,0) and (0,k) is 9 sq. u...

    Text Solution

    |

  19. The value of determinant |(a-b ,b+c,a),(b-a,c+a,b),(c-a,a+b,c)| is

    Text Solution

    |

  20. If [[ 2 x , 5],[ 8 , x ]] = [[6 , -2 ],[7 , 3 ]], then, x=

    Text Solution

    |