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A=[[2,1],[4,1]]; B=[[3,4],[2,3]] & c=[[3...

`A=[[2,1],[4,1]]; B=[[3,4],[2,3]]` & `c=[[3,-4],[-2,3]]`, `tr(A)+tr[(ABC)/2]+tr[(A(BC)^2)/4]+tr[(A(BC)^2)/8]+.....oo` is:

A

6

B

9

C

12

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`BC=[(3,4),(2,3)][(3,-4),(-2,3)]impliesB=[(1,0),(0,1)]`
`implies tr(A)+tr((ABC)/2)+tr((A(BC)^(2))/4)+tr ((A(BC)^(3))/8)+...+ oo`
`=tr (A)+tr (A/2)+tr (A/2^(2))+...`
`=tr (A)+1/2 tr (A)+1/2^(2) tr (A)...`
`=(tr (A))/(1-(1//2))`
`=2tr (A)=2(2+1)=6`
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