Home
Class 11
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

`nA-(n-2)I`

D

`nA-2I`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    AAKASH SERIES|Exercise ALGEBRA OF MATRICES -PRACTICE EXERCISE|41 Videos
  • MATRICES

    AAKASH SERIES|Exercise DETERMINANTS- EXERCISE - I|15 Videos
  • MATRICES

    AAKASH SERIES|Exercise ALGEBRA OF MATRICES -EXERCISE - I|47 Videos
  • MATHEMATICAL INDUCTION

    AAKASH SERIES|Exercise PRACTICE SHEET (EXERCISE-I) LEVEL-I (Principle of Mathematical Induction) (Straight Objective Type Questions)|55 Videos
  • MAXIMA & MINIMA

    AAKASH SERIES|Exercise EXERCISE-III|35 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) .

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

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

If n is 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).

For any integer n ge 2 , let I_(n) = int tan^(n) xdx . If I_(n) =1/a tan^(n-1)x - bI_(n-2) for n ge 2 , then the ordered pair (a,b) equals to

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 alpha and beta are the greatest divisors of n(n^(2)-1) and 2n(n^(2)+2) respectively for all n in N , then alpha beta=

AAKASH SERIES-MATRICES -ALGEBRA OF MATRICES - EXERCISE - II
  1. If A=((coshtheta,sinhtheta),(sinhtheta,coshtheta)) and ninN then A^(n)...

    Text Solution

    |

  2. If A=[(1,1,0),(0,1,1),(0,0,1)] and ninN then A^(n)=

    Text Solution

    |

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

    Text Solution

    |

  4. If A=[(i,0,0),(0,i,0),(0,0,i)] then for ninN,A^(4n+1)=

    Text Solution

    |

  5. If A=((0,0),(1,1)) then the value of A+A^(2)+A^(3)+ . . . .A^(n)=

    Text Solution

    |

  6. If A=((2,-2,-4),(-1,3,4),(1,-2,k)) is an idempotent matrix then k =

    Text Solution

    |

  7. IF A=[{:(2,4),(-1,k):}] and A^2=0 then find the value of k

    Text Solution

    |

  8. A=[(1+i,2-3i,4),(7+2i,-i,3-2i)] then the conjugate of A is

    Text Solution

    |

  9. If A is a skew-symmetric matrix and n is odd positive integer, then A^...

    Text Solution

    |

  10. If [(1,-tan theta),( tan theta,1)][(1,tan theta),(-tan theta, 1)]^-1=[...

    Text Solution

    |

  11. If [[x,4,-1]][(2,1,0),(1,0,2),(0,2,4)][(x),(4),(-1)]=0 then x=

    Text Solution

    |

  12. If A=[a(ij)] is a skew symmetric matrix of order 'n' then suma(ii)=

    Text Solution

    |

  13. The number of 2xx2 matrices that can be formed by using 1,2,3,4 withou...

    Text Solution

    |

  14. If a matrix has 13 elements, then the possible dimensions (orders) of ...

    Text Solution

    |

  15. Statement - I, The matrix [(1,-3,-4),(-1,3,4),(1,-3,-4)] is a nilpote...

    Text Solution

    |

  16. Statement - I If A=[(x,1),(1,0)] is an Involutory matrix then x=0 St...

    Text Solution

    |

  17. Arrange the following matrices in ascending order of value of their tr...

    Text Solution

    |

  18. If A is any square matrix. Observe the following lists and matching fr...

    Text Solution

    |

  19. Assertio (A) : If [(x,1),(1,0)] is an idempotent matrix then x=0 Rea...

    Text Solution

    |

  20. Assertion (A) : If A=[(x,3,-10),(-3,y,9),(10,-9,z)] is a skew symmetr...

    Text Solution

    |