Home
Class 12
MATHS
If A and P are different matrices of ord...

If `A` and `P` are different matrices of order `n` satisfying `A^(3)=P^(3)` and `A^(2)P=P^(2)A` (where `|A-P| ne 0`) then `|A^(2)+P^(2)|` is equal to

A

`n`

B

`0`

C

`|A||P|`

D

`|A+P|`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `(A^(2)+P^(2))(A-P)=A^(3)-A^(2)P+P^(2)A-P^(3)`
`=(A^(3)-P^(2))+(P^(2)A-A^(2)P)`
`=0`
`:. |(A^(2)+P^(2))(A-P)|=0`
`:. |A^(2)+P^(2)|=0` `( :' |A-P| ne 0)`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    CENGAGE|Exercise Multiple Correct Answer|7 Videos

  • MATRICES

    CENGAGE|Exercise Solved Examples And Exercises|165 Videos

  • MATRICES

    CENGAGE|Exercise JEE Advanced Previous Year|26 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE|Exercise Single Correct Answer Type|46 Videos

Similar Questions

Explore conceptually related problems

If P = {2, 3}, then P xx P is equal to

Let P and Q be 3xx3 matrices with P!=Q. If P^(3)=Q^(3) and P^(2)Q=Q^(2)P, then determinant of (P^(2)+Q^(2)) is equal to (1)2(2)1(3)0(4)1

The number of non-negative integers 'n' satisfying n^(2)=p+q and n^(3)=p^(2)+q^(2) where p and q are integers

If S_(m)=m^(2) p and S_(n)=n^(2)p , where m ne n in an AP then prove that S_(p) =P^(3)

Suppose P and Q are two different matrices of order 3 xx n and n xx p ,then the order of the matrix P xx Q is ?

Suppose P and Q are two different matrices of order 3xx n " and " n xx p , then the order of the matrix P xx Q is ?

CENGAGE-MATRICES-Single correct Answer
  1. If AB+BA=0, then which of the following is equivalent to A^(3)-B^(3)

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. If A=[{:(costheta,sintheta),(sintheta,-costheta):}], B=[{:(1,0),(-1,1)...

    Text Solution

    |

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

    Text Solution

    |

  9. Suppose A and B are two non singular matrices such that B != I, A^6 = ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. If A and B are two non singular matrices and both are symmetric and co...

    Text Solution

    |

  16. If A is a square matrix of order 3 such that |A|=2, then |(adjA^(-1))^...

    Text Solution

    |

  17. Let matrix A=[{:(x,y,-z),(1,2,3),(1,1,2):}] , where x,y,z in N. If |ad...

    Text Solution

    |

  18. A be a square matrix of order 2 with |A| ne 0 such that |A+|A|adj(A)|=...

    Text Solution

    |

  19. If A is a skew symmetric matrix, then B=(I-A)(I+A)^(-1) is (where I is...

    Text Solution

    |

  20. If A=[{:(3,-3,4),(2,-3,4),(0,-1,1):}] , then the trace of the matrix A...

    Text Solution

    |