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

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
`f(x)=(1+x)/(1-x)`
or `(1-x) f(x)=1+x`
`implies (I-A)f(A)=(I+A)`
`implies 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)])`
`=([(0,2),(2,0)][(2,2),(2,2)])/(-4)`
`=([(4,4),(4,4)])/(-4)`
`=[(-1,-1),(-1,-1)]`
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