Home
Class 12
MATHS
If A=[i-i-i i]a n dB=[1-1-1 1],t h e nA^...

If `A=[i-i-i i]a n dB=[1-1-1 1],t h e nA^8` equals `4B` b. `128 B` c. `-128 B` d. `-64 B`

A

4B

B

128B

C

`-128` B

D

`-64`B

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`A=iB`
or `A^(2)=(iB)^(2)=i^(2)B^(2)=-B^(2)=- [(2,-2),(-2,2)]=-2B`
or `A^(4)=(-2B)^(2)=4B^(2)=4(2B)=8B`
or `(A^(4))^(2)=(8B)^(2)`
or `A^(8)=64 B^(2)=128 B`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    CENGAGE|Exercise Exercise (Multiple)|33 Videos

  • MATRICES

    CENGAGE|Exercise Exercise (Comprehension)|18 Videos

  • MATRICES

    CENGAGE|Exercise Exercise 13.5|17 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE|Exercise Single Correct Answer Type|46 Videos

Similar Questions

Explore conceptually related problems

If A=[[i,-i],[-i, i ]] and B=[[1,-1],[-1,1]] ,then A^( 8 ) equals,(where i=sqrt(-1) ) 4B 128 B -128 B -64 B

If A=[{:(i,-i),(-i, i):}] and B=[{:(1,-1),(-1,1):}] , then A^(4) equals to-

If A=([i,-i],[-i,i]) , B=([1,-1],[-1,1]) , A^(8)=KB and K=a^(b) then a+b=

If A = 1/ sqrt(3) [[1,1+i],[1-i,1]] then A(bar(A)^T) equals : a. O b. I c. -I d. 2I

If A=[[a+i b, c+i d],[-c+i d, a-i b]]a n da^2+b^2+c^2+d^2=1,t h e nA^(-1) is equal to a.[[a+i b,-c+i d],[-c+i d, a-i b]] b. [[a-i b,-c-i d],[-c-i d, a+i b]] c. [[a+i b,-c-i d],[-c+i d, a-i b]] d. none of these

If a=1+i, then a^(2) equals 1-i b.2i .(1+i)(1-i) d.(i-1)

If log_(32)x=0.8 , t h e n x is equal to a. 25.6 b. 16 c. 10 d. 12.8

CENGAGE-MATRICES-Exercise (Single)
  1. If A=[a b0a] is nth root of I2, then choose the correct statements: If...

    Text Solution

    |

  2. If [alphabetagamma-alpha] is to be square root of two-rowed unit matri...

    Text Solution

    |

  3. If A=[i-i-i i]a n dB=[1-1-1 1],t h e nA^8 equals 4B b. 128 B c. -128 B...

    Text Solution

    |

  4. If [(2,-1),(1,0),(-3,4)]A=[(-1,-8,-10),(1,-2,-5),(9,22,15)] , then sum...

    Text Solution

    |

  5. For each real x, -1 lt x lt 1. Let A(x) be the matrix (1-x)^(-1) [(1,-...

    Text Solution

    |

  6. Let A=[0-tan(alpha//2)tan(alpha//2)0] and I be the identity matrix ...

    Text Solution

    |

  7. The number of solutions of the matrix equation X^2=[1 1 2 3] is a. mor...

    Text Solution

    |

  8. If A=[a b c d] (where b c!=0 ) satisfies the equations x^2+k=0,t h e n...

    Text Solution

    |

  9. A=[[2,1],[4,1]]; B=[[3,4],[2,3]] & c=[[3,-4],[-2,3]], tr(A)+tr[(ABC)/2...

    Text Solution

    |

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

    Text Solution

    |

  11. If A and B are square matrices of order n , then prove that Aa n dB wi...

    Text Solution

    |

  12. Matrix A such that A^2=2A-I ,w h e r eI is the identity matrix, the fo...

    Text Solution

    |

  13. Let A=[(0, alpha),(0,0)] and (A+I)^(50) -50A=[(a,b),(c,d)]. Then the v...

    Text Solution

    |

  14. If Z is an idempotent matrix, then (I+Z)^(n)

    Text Solution

    |

  15. if Aa n dB are squares matrices such that A^(2006)=Oa n dA B=A+B ,t h ...

    Text Solution

    |

  16. If matrix A is given by A=[[6,11] , [2,4]] then determinant of A^(2005...

    Text Solution

    |

  17. If A is a non-diagonal involutory matrix, then

    Text Solution

    |

  18. If A and B are two nonzero square matrices of the same order such that...

    Text Solution

    |

  19. If A and B are symmetric matrices of the same order and X=AB+BA and Y...

    Text Solution

    |

  20. If A ,B ,A+I ,A+B are idempotent matrices, then A B is equal to

    Text Solution

    |