Home
Class 12
MATHS
A square matrix P satisfies P^(2)=I-P wh...

A square matrix `P` satisfies `P^(2)=I-P` where `I` is identity matrix. If `P^(n)=5I-8P`, then `n` is

A

4

B

5

C

6

D

7

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    DISHA PUBLICATION|Exercise Exercise 1: Concept Builder (Topic 3)|23 Videos

  • MATHEMATICAL REASONING

    DISHA PUBLICATION|Exercise Exercise-2 : Concept Applicator|30 Videos

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    DISHA PUBLICATION|Exercise Exercise-2 Concept Applicator|20 Videos

Similar Questions

Explore conceptually related problems

A square matrix P satisfies P^(2)=I-p where I is the identity matrix and p^(x)=5I-8p, then x

A square matrix P satisfies P^(2)=I-2P where I is identity matrix.If P^(2)+P^(3)+P^(4)=a^(2)I-b^(2)P then a^2+b^2=

A square matrix P satisfies P^(2)=I-2P where I is identity matrix. If P^(2)+P^(3)+P^(4)=a^(2)I-b^(2)P ,then

A square matrix M of order 3 satisfies M^(2)=I-M , where I is an identity matrix of order 3. If M^(n)=5I-8M , then n is equal to _______.

A square matrix P satisfies P^2=I-2P where I is the identify matrix if P^(2)+P^(3)+P^(4)=a^(2)I-b^(2)P then a,b=

A square matrix A of order 3 satisfies A^(2)=I-2A , where I is an identify matrix of order 3. If A^(n)=29A-12I , then the value of n is equal to

Let A=[("tan"pi/3,"sec" (2pi)/3),(cot (2013 pi/3),cos (2012 pi))] and P be a 2 xx 2 matrix such that P P^(T)=I , where I is an identity matrix of order 2. If Q=PAP^(T) and R=[r_("ij")]_(2xx2)=P^(T) Q^(8) P , then find r_(11) .

Matrix A is such that A^(2)=2A-I , where I is the identify matrix. Then for n ne 2, A^(n)=

DISHA PUBLICATION-MATRICES-Exercise 2: Concept Applicator
  1. If A1, A2, , A(2n-1)a r en skew-symmetric matrices of same order, the...

    Text Solution

    |

  2. For k=1/sqrt(50), the value of a, b, c such that PP' = I, where P=[(2/...

    Text Solution

    |

  3. IfA^(k)= 0 (Ais nilpotent with index k), (I-A)^(p)=I+A+A^(2)+. . .+A^(...

    Text Solution

    |

  4. If A and B are two square matrices such that B=-A^(-1)BA, then (A+B)^(...

    Text Solution

    |

  5. If A=[(1,-1),(2,-1)] and B=[(1,a),(4,b)] and (A+B)^(2)=A^(2)+B^(2). ...

    Text Solution

    |

  6. If A is a square matrix such that A A^T=I=A^TA, then A is

    Text Solution

    |

  7. If Aa n dB are symmetric matrices of the same order and X=A B+B Aa n d...

    Text Solution

    |

  8. [{:(2x+y,4x),(5x-7,4x):}]=[{:(7,7y-13),(y,x+6):}] then the value of x,...

    Text Solution

    |

  9. Given that [(1,omega,omega^(2)),(omega,omega^(2),1),(omega^(2),1,omega...

    Text Solution

    |

  10. If {:A=[(alpha,0),(1,1)]andB=[(1,0),(5,1)]:}, then te value of alpha f...

    Text Solution

    |

  11. [[i,0,0],[0,i,0],[0,0,i]] then A^(4n+1) =.... n in N

    Text Solution

    |

  12. The matrix A=[0-5 8 5 0 12-8-12 0] is a (a) diagonal matrix (b) symmet...

    Text Solution

    |

  13. If A=[(alpha,0),(1,1)] and B=[(9,a),(b,c)] and A^(2)=B, then the value...

    Text Solution

    |

  14. Find the value of k so that A^2=8A+kI where A=[(1,0),(-1,7)].

    Text Solution

    |

  15. A square matrix P satisfies P^(2)=I-P where I is identity matrix. If P...

    Text Solution

    |

  16. If A(alpha)=[(cosalpha,-sinalpha),(sinalpha,cosalpha)], then

    Text Solution

    |

  17. If B is an idempotent matrix, and A=I-B, then

    Text Solution

    |

  18. If B=[(3,4),(4,3)] and C=[(3,-4),(-2,3)] and X=BC, find X^(n)

    Text Solution

    |

  19. If A=[(1,0),(1//2,1)], A^(400) is equal to

    Text Solution

    |

  20. Let A=[(0,alpha),(0,0)] and (A+I)^(50)-50A=[(a,b),(c,d)], find abc+abd...

    Text Solution

    |