Home
Class 12
MATHS
If A^(2)=2A-I then for n>=2,A^(n)=...

If `A^(2)=2A-I` then for `n>=2,A^(n)=`

A

`nA-(n-1)I`

B

`nA-I`

C

`2^(n-1)A-(n-1)I`

D

`2^(n-1)A-I`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 1B MCQ (DETERMINANTS)|189 Videos

  • MATRICES

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 1C MCQ (INVERSE MATRIX)|88 Videos

  • MATRICES

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 MCQ (SPECIAL TYPES QUESTIONS) SET -4|8 Videos

  • MATHEMATICAL REASONING [APPENDIX - 4]

    DIPTI PUBLICATION ( AP EAMET)|Exercise Exercise|150 Videos

  • MEASURES OF DISPERSION

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE-2 ( SET -4)|2 Videos

Similar Questions

Explore conceptually related problems

If n is an integer and z=cis theta,(theta ne (2n+1)pi/2), then show that (z^(2n)-1)/(z^(2n)+1)=i tan n theta) .

Show that If I _(n) =int cos ^(n) x dx, then show that I_(n) =1/n cos ^(n-1) x sin x + (n-1)/(n ) I_(n-2).

If I_(n)=int_(0)^(pi//4) tan^(n)theta d theta for 1,2,3,… then I_(n-1)+I_(n+1)=

Assertion (A) : If I_(n) = int tan^(n) xdx then 5 (I_(4) + I_(6)) = tan^(5) x Reason (R) : int tan^(n) " xdx then " I_(n) = (tan^(n-1)x)/(n) -I_(n- 2) " where n " in N The correct answer is

If I_(n)=int (t^(n))/(1+t^(2))dt, then I_(n-2)=

If n is integer then show that (1 + i)^(2n) + (1 - i)^(2n) = 2 ^(n+1) cos . (npi)/2 .

For any integer n le 2 let I_(n)= int x dx . If I_(n)=(1)/(a)tan^(n-1)x-bl_(a-2) for n ge 2 , then ordered pair (a,b) =

DIPTI PUBLICATION ( AP EAMET)-MATRICES-EXERCISE 1A MCQ (ALGEBRA OF MATRICES)
  1. If A=[(3,-4),(1,-1)] then A^(T)=

    Text Solution

    |

  2. [(2,-1),(3,-2)]^(n)=[(1,0),(0,1)] if n is

    Text Solution

    |

  3. If A^(2)=2A-I then for n>=2,A^(n)=

    Text Solution

    |

  4. fi A=[(1,1),(1,1)] then A^(3)=

    Text Solution

    |

  5. If A=[(1,0),(1,1)] and I=[(1,0),(0,1)] then which one of the following...

    Text Solution

    |

  6. Find the rank of the matrix A=[(1,4),(0,1)],

    Text Solution

    |

  7. If A=[(1,0,0),(1,0,1),(0,1,0)] Then tra(A)

    Text Solution

    |

  8. If A=[(1,1,0),(0,1,1),(0,0,1)] then A^(2)=

    Text Solution

    |

  9. if n is a positive integer and A=[(a,0,0),(0,b,0),(0,0,c)] then A^(n) ...

    Text Solution

    |

  10. If A = [(cos theta, sin theta),(-sin theta, cos theta)] then show that...

    Text Solution

    |

  11. If A=[(cos theta, sin theta),(- sin theta, cos theta)] then lim(nto oo...

    Text Solution

    |

  12. If A=[(-cos theta, sin theta),(sin theta, cos theta)] then IAI=

    Text Solution

    |

  13. If A=[(cos^(2) alpha, cos alpha sin alpha),(cos alpha sin alpha,sin^(2...

    Text Solution

    |

  14. If alpha-beta=(2n+1)(pi)/2, n epsilon Z then [(cos^(2) alpha, cos alph...

    Text Solution

    |

  15. If A(alpha)=[(cos alpha, sin alpha),(-sin alpha, cos alpha)], then A(a...

    Text Solution

    |

  16. If A=[(a,b),(c,d)],I=[(1,0),(0,1)] then A^(2)-(a+d)A=

    Text Solution

    |

  17. If A=[(0,c,-b),(-c,0,a),(b,-a,0)] then A^(3)=

    Text Solution

    |

  18. If A=[(1,1,3),(5,2,6),(-2,-1,-3)] then A^(3)=

    Text Solution

    |

  19. If A=[(1,1,-2),(0,1,4),(2,3,1)] then A^(3)-3A^(2)-5A=

    Text Solution

    |

  20. A=[{:(1,2,2),(2,1,2),(2,2,1):}], then A^(3) - 4A^(2) -6A is equal to

    Text Solution

    |