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If `A=[[i,-i],[-i ,i]] and B=[[1,-1],[-1 ,1]], t hen ,A^8` equals a.`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`
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