Home
Class 12
MATHS
If A=[i0 0i],\ n in N , then A^(4n) equ...

If `A=[i0 0i],\ n in N` , then `A^(4n)` equals `[0i i0]` (b) `[0 0 0 0]` (c) `[1 0 0 1]` (d) `[0i i0]`

Text Solution

Verified by Experts

Given: `A=[(i,0),(0,i)], n in N`
Then
`A^2=[(i,0),(0,i)][(i,0),(0,i)]`
`A^2=[(i^2,0),(0,i^2)]`
As `i^2=-1`
then
`A^2=[(-1,0),(0,-1)]`
`A^4=A^2.A^2=[(-1,0),(0,-1)][(-1,0),(0,-1)]`
...
Promotional Banner

Topper's Solved these Questions

  • ADJOINTS AND INVERSE OF MATRIX

    RD SHARMA|Exercise QUESTION|1 Videos

  • ALGEBRA OF VECTORS

    RD SHARMA|Exercise Solved Examples And Exercises|331 Videos

Similar Questions

Explore conceptually related problems

If {:A=[(i,0),(0,i)]:},n in N" then " A^(4n) equal

If A=[[i, 0], [0, (i)/(2)]] , then A^(-1)=

If A=[[i,0],[0,i]];i=sqrt(-1), then A^(n) is equal to

1.If A=[[i,0],[0,-i]] then show that A^(2)=-I

If A = [(-i,0),(0,i)] then A ' A is equal to

If A=[[0,0],[0,i]], where i=sqrt(-1), then

If I=[[1,0],[0,1]] , then I^4=

If A=[(1,a),(0, 1)] , then A^n (where n in N) equals [(1,n a),(0, 1)] (b) [(1,n^2a),(0, 1)] (c) [(1,n a),(0 ,0)] (d) [(n,n a),(0,n)]

If for a matrix A,A^2+I=0, where I is an identity matrix then A equals (A) [(1,0),(0,1)] (B) [(-1,0),(0,-1)] (C) [(1,2),(-1,1)] (D) [(-i,0),(0,-i)]

RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. If A=[3 5 7 9] is written as A=P+Q , where P is symmetric and Q is sk...

    Text Solution

    |

  2. If A=[(1 ,0, 0),(0, 1,0),( a,b, -1)] , then A^2 is equal to (a) a n...

    Text Solution

    |

  3. If A=[i0 0i],\ n in N , then A^(4n) equals [0i i0] (b) [0 0 0 0] (c) ...

    Text Solution

    |

  4. If A and B are two matrices such that A B=A and B A=B , then B^...

    Text Solution

    |

  5. If A B=A and B A=B , where A and B are square matrices, then B^2=B ...

    Text Solution

    |

  6. If A and B are two matrices such that AB=B and BA=A , then A^2+B^2=

    Text Solution

    |

  7. If [(cos\ (2pi)/7,-sin\ (2pi)/7),(sin\ (2pi)/7,cos\ (2pi)/7)]^k=[(1,0)...

    Text Solution

    |

  8. If the matrix A B is zero, then It is not necessary that either A=O...

    Text Solution

    |

  9. Let A=[(a,0, 0),( 0,a,0),( 0, 0,a)] , then A^n is equal to [(a^n,0,...

    Text Solution

    |

  10. If A ,\ B are square matrices of order 3,\ A is non-singular and A ...

    Text Solution

    |

  11. If A=[(n,0 ,0),( 0,n,0),( 0, 0,n)] and B=[(a1,a2,a3),(b1,b2,b3),(c1,c2...

    Text Solution

    |

  12. If A=[(1,a),(0, 1)] , then A^n (where n in N) equals [(1,n a),(0,...

    Text Solution

    |

  13. If A=[1 2x0 1 0 0 0 1] and B=[1-2y0 1 0 0 0 1] and A B=I3 , then x+y e...

    Text Solution

    |

  14. If A=[1-1 2-1] , B=[a1b-1] and (A+B)^2=A^2+B^2 , then values of a and ...

    Text Solution

    |

  15. If A=[alphabetagamma-alpha] is such that A^2=I , then 1+alpha^2+betaga...

    Text Solution

    |

  16. If S=[S(i j)] is a scalar matrix such that s(i i)=ka n dA is a square ...

    Text Solution

    |

  17. If a square matrix such that A^2=A , then (I+A)^3-7A is equal to A ...

    Text Solution

    |

  18. If a matrix A is both symmetric and skew-symmetric, then A is a

    Text Solution

    |

  19. The matrix [(0, 5,-7),(-5, 0, 11),( 7,-11, 0)] is (a) a skew-symmetr...

    Text Solution

    |

  20. If A is a square matrix, then A A is a (a) skew-symmetric matrix (b)...

    Text Solution

    |