Home
Class 11
MATHS
If A=[{:(omega,0),(0,omega):}], where om...

If `A=[{:(omega,0),(0,omega):}]`, where `omega` is cube root of unity, then what is `A^(100)` equal to ?

A

A

B

`-A`

C

O

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`A={:omega[(1,0),(0,1)]=omegaI_2:}`
`:. A^100=omega^100(I_2)^100=omega^100I_2=omegaI_2=A`.
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Assertion Reason Type|12 Videos

  • MATRICES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|79 Videos

  • MATRICES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • LOGARITHMS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|21 Videos

  • MEAN VALUE THEOREMS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|28 Videos

Similar Questions

Explore conceptually related problems

If omega is a cube root of unity, then 1+omega = …..

If omega is a cube root of unity, then omega^(3) = ……

If omega is a cube root of unity, then 1+ omega^(2)= …..

If omega is a cube root of unity, then omega + omega^(2)= …..

If A =({:( 1,1,1),( 1,omega ^(2) , omega ),( 1 ,omega , omega ^(2)) :}) where omega is a complex cube root of unity then adj -A equals

If 1,omega,omega^2 are the cube roots of unity, then /_\ is equal to.....

If |z-1|lt=2a n d|omegaz-1-omega^2|=a (where omega is a cube root of unity) , then complete set of values of a

Let A=[(omega,-omega),(-omega,omega)] where w is a complex cube root of unity, B =[(1,-1),(-1,1) and A^9=2^kB , where k = ....

Elements of a matrix A of order 10 x 10 are defined as a_(ij)=omega^(i+j) (where omega is cube root unity), then tr(A) of matrix is

If 1, omega, omega^(2) are three cube roots of unity, prove that (1 + omega^(2))^(4)= omega

OBJECTIVE RD SHARMA ENGLISH-MATRICES-Section I - Solved Mcqs
  1. If A a 3xx3 amtrix and B is its adjoint such that |B| = 64, then |A| i...

    Text Solution

    |

  2. If A=1/3|[1, 2, 2], [2, 1,-2],[a,2,b]| is an orthogonal matrix, then ...

    Text Solution

    |

  3. If A=[{:(omega,0),(0,omega):}], where omega is cube root of unity, the...

    Text Solution

    |

  4. If A^(3)=O, then prove that (I-A)^(-1) =I+A+A^(2).

    Text Solution

    |

  5. if A=[{:(0,1,-1),(2,1,3),(3,2,1):}]then (A(adjA)A^-1)A is equal to

    Text Solution

    |

  6. If A is non-singular and (A-2I)(A-4I)=0 , then ,1/6A+4/3A^(-1) is equa...

    Text Solution

    |

  7. If A is an invertible matrix of order 3xx3 such that |A|=2 . Then, ...

    Text Solution

    |

  8. If A and B are squre 3xx3 such that A is an orthogonal matrix and B is...

    Text Solution

    |

  9. If A=|[alpha,2], [2,alpha]| and |A|^3=125 , then the value of alpha ...

    Text Solution

    |

  10. about to only mathematics

    Text Solution

    |

  11. If A=[(1,0,0),(0,1,1),(0,-2,4)] , 6A^(-1)=A^2+cA+dI, then (c,d) is :

    Text Solution

    |

  12. Let {:A=[(1,0,0),(2,1,0),(3,2,1)]:}and U1,U2,U3 be column matrices sat...

    Text Solution

    |

  13. If U={:[(1,2,2),(-2,-1,-1),(1,-4,-3)]:}' ,sum of elements of inverse o...

    Text Solution

    |

  14. If U is same as in Example 50, then the value of {:[(3,2,0)]U[(3),(2),...

    Text Solution

    |

  15. If A and B f are square matrices of size nxxn such that A^(2) - B^(2...

    Text Solution

    |

  16. If A and B are any two different square matrices of order n with A^3=B...

    Text Solution

    |

  17. Let A=[(0,0,-1),(0,-1,0),(-1,0,0)] Then only correct statement about t...

    Text Solution

    |

  18. Let A=[(1,-1,1),(2,1,-3),(1,1,1)] and 10 B=[(4,2,2),(-5,0,alpha),(1,-2...

    Text Solution

    |

  19. Let A= [[5,5alpha,alpha],[0,alpha,5alpha],[0,0,5]] . If |A^2|...

    Text Solution

    |

  20. If {:A=alpha[(1,1+i),(1-i,-1)]:}a in R, is a unitary matrix then alpha...

    Text Solution

    |