Home
Class 12
MATHS
if A=[[i,0] , [0,i]] where i=sqrt(-1) an...

if `A=[[i,0] , [0,i]]` where `i=sqrt(-1)` and `x in N` then `A^(4x)` equals to:

Text Solution

Verified by Experts

`A^(2)=[(i,0),(0,i)][(i,0),(0,i)]=[(i^(2),0),(0,i^(2))]=[(-1,0),(0,-1)]`
`A^(4)=[(-1,0),(0,-1)][(-1,0),(0,-1)]=[(1,0),(0,1)]=I`
`implies A^(4n)=I^(n)=I`
Promotional Banner

Topper's Solved these Questions

  • MATHMETICAL REASONING

    CENGAGE PUBLICATION|Exercise Archives|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|7 Videos

Similar Questions

Explore conceptually related problems

If s(n)= i^n+i^(-n) where i=sqrt(-1) and n is an integer then the total number of distinct values of S(n) is

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

If x=a+bi is a complex number such that x^2=3+4i and x^3=2+11i , where i=sqrt-1 , then (a+b) equal to

If I=int sqrt((5-x)/(2+x)) dx, then equal

if I=int_0^a sqrt((a-x)/(a+x))dx, agt0 Then I equals

if I=int_8^15 dx/((x-3)sqrt(x+1)) then I equals

if I=int_0^(1.7)[x^2]dx then I equals

If i=sqrt-1 and n is a positive integer, then i^(n)+i^(n+1)+i^(n+3_ is equal to

Let f: RR to RR be a function defined by f(x)={{:([x],x le2),(0,x gt2):} , where [x] is the greatest integer less than or equal to x. If I=int_(-1)^(2)(xf(x^(2)))/(2+f(x+1))dx , then the value of (4I-1) is-

I=inte^x/(e^x+1)^(1//4)dx is equal to

CENGAGE PUBLICATION-MATRICES-All Questions
  1. Consider the matrices A=[(4,6,-1),(3,0,2),(1,-2,5)], B=[(2,4),(0,1),...

    Text Solution

    |

  2. Let A=B B^(T)+C C^(T), where B=[(cos theta),(sin theta)], C=[(sin thet...

    Text Solution

    |

  3. if A=[[i,0] , [0,i]] where i=sqrt(-1) and x in N then A^(4x) equals to...

    Text Solution

    |

  4. If A = [[1,2],[3,-5]] and B=[[1,0],[0,2]] and X is a matrix such that ...

    Text Solution

    |

  5. Find the matrix X so that X[1 2 3 4 5 6]=[-7-8-9""""""2""""""4""""6]

    Text Solution

    |

  6. If A=[[costheta,sintheta],[-sintheta,costheta]],then Lim(ntooo)1/nA^n ...

    Text Solution

    |

  7. A=[(3,a,-1),(2,5,c),(b,8,2)] is symmetric and B=[(d,3,a),(b-a,e,-2b-c)...

    Text Solution

    |

  8. If A and B are matrices of the same order, then A B^T-B A^T is a (a)...

    Text Solution

    |

  9. If A and B are square matrices such that AB = BA then prove that A^(3)...

    Text Solution

    |

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

    Text Solution

    |

  11. If B ,C are square matrices of order na n difA=B+C ,B C=C B ,C^2=O , t...

    Text Solution

    |

  12. Let A be any 3xx2 matrix. Then prove that det. (A A^(T))=0.

    Text Solution

    |

  13. Let A be a matrix of order 3, such that A^(T)A=I. Then find the value ...

    Text Solution

    |

  14. A and B are different matrices of order n satisfying A^(3)=B^(3) and A...

    Text Solution

    |

  15. Statement 1: if D=diag[d1, d2, ,dn],then D^(-1)=diag[d1^(-1),d2^(-1),...

    Text Solution

    |

  16. Point P(x, y) is rotated by an angle theta in anticlockwise direction....

    Text Solution

    |

  17. How many different diagonal matrices of order n can be formed which ar...

    Text Solution

    |

  18. How many different diagonal matrices of order n can be formed which ar...

    Text Solution

    |

  19. If A and B are n-rowed unitary matrices,then AB and BA are also unitar...

    Text Solution

    |

  20. By the method of matrix inversion, solve the system. [(1,1,1),(2,5,7...

    Text Solution

    |