Home
Class 11
MATHS
If A=((x,0,0),(0,x,0),(0,0,x)) then A^(n...

If `A=((x,0,0),(0,x,0),(0,0,x))` then `A^(n)=(ninN)`

A

`x^(n)A`

B

`x^(n-1)A`

C

`"x A"`

D

`-x^(n)A`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • MATRICES

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

  • MATRICES

    AAKASH SERIES|Exercise DETERMINANTS- EXERCISE - II|52 Videos

  • MATRICES

    AAKASH SERIES|Exercise ALGEBRA OF MATRICES - EXERCISE - II|34 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 A=[(1,1,0),(0,1,1),(0,0,1)] and ninN then A^(n)=

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

If A=[(cosx, sin x, 0),(-sin x, cosx, 0),(0,0,1)]=f(x) then A^(T)=

If F(x)=[(cosx,-sinx,0),(sinx,cosx,0),(0,0,1)] and G(x)=[(cosx,0,sinx),(0,1,0),(-sinx,0,cosx)] then [F(x)G(x)]^(-1) =

If F(x)=[(cosx,-sinx,0),(sinx,cosx,0),(0,0,1)] , show that F(x) F(y)=F(x+y) .

The area of the triangle formed by (0, 0), (a^(x^(2)), 0), (0, a^(6x)) is 1//2a^(5) sq.unit then x =

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

AAKASH SERIES-MATRICES -ALGEBRA OF MATRICES -PRACTICE EXERCISE
  1. Let A be a square matrix. Then A+A^(T) will be

    Text Solution

    |

  2. If A and B are two symmetric matrices then AB + BA is

    Text Solution

    |

  3. If A=((x,0,0),(0,x,0),(0,0,x)) then A^(n)=(ninN)

    Text Solution

    |

  4. If A is a symmetric matrix and n epsilon N, then A^(n) is

    Text Solution

    |

  5. If A=[(0,1),(1,0)] then A^(2004)=

    Text Solution

    |

  6. If A=[(1,3),(3,4)] and A^(2)-kA-5I(2)=O then k=

    Text Solution

    |

  7. If the matrix A=((1,-1),(-1,1)) then A^(n+1)=

    Text Solution

    |

  8. [(2,-1),(3,-2)]^(n)=[(1,0),(0,1)] if n is

    Text Solution

    |

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

    Text Solution

    |

  10. IF A=[{:(costheta,sintheta),(-sintheta,costheta):}] then show that for...

    Text Solution

    |

  11. If A=[(0,a+1,b-2),(2a-1,0,c-2),(2b+1,2+x,0)] is skew symmetric then a+...

    Text Solution

    |

  12. If A is a skew symmetric matrix and n is an even positive integer then...

    Text Solution

    |

  13. A=[a(ij)](3xx3) is a square matrix so that a(ij)=i^(2)-j^(2) then A is...

    Text Solution

    |

  14. A is a symmetric matrix or skew symmetric matrix. Then A^(2)is

    Text Solution

    |

  15. If A="diag "["1 -1 2"],B=" diag "["2 3 -1"] and 3A+4B = diag [...

    Text Solution

    |

  16. Observe the following lists and matching from List - I to List - II is...

    Text Solution

    |

  17. If A=[(a,b),(b,a)] and A^(2)=[(alpha, beta),(beta, alpha)] then

    Text Solution

    |

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

    Text Solution

    |

  19. Let ((1,2),(3,4)) and B=((a,0),(0,b)), a, b epsilon N. Then

    Text Solution

    |

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

    Text Solution

    |