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If A=[(1,2),(2,1)] and f(x)=(1+x)/(1-x),...

If `A=[(1,2),(2,1)]` and `f(x)=(1+x)/(1-x)`, then f(A) is

A

`[[1 ,1],[1,1]]`

B

`[[2 ,2],[2,2]]`

C

`[[-1 ,-1],[-1,-1]]`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`because f(x) = (1+x)/(1-x)`
`rArr (1-x) f(x) = 1 +x`
`rArr (I-A)f(A) = (I+A)`
` rArr f(A) = (I-A)^(-1) (I+A)`
`([[1,0],[0,1]]-[[1,2],[2,1]])^(-1)([[1,0],[0,1]]+[[1,2],[2,1]])`
`[[0,-2],[-2,0]]^(-1)[[2,2],[2,2]]=-1/4[[0,2],[2,0]][[2,2],[2,2]]`
`=-1/4 [[4,4],[4,4]]=[[-1,-1],[-1,-1]]`
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