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For each real x, -1 lt x lt 1. Let A(x) ...

For each real `x, -1 lt x lt 1`. Let A(x) be the matrix `(1-x)^(-1) [(1,-x),(-x,1)]` and `z=(x+y)/(1+xy)`. Then

A

`A(z)=A(x) A(y)`

B

`A(z)=A(x)-A(y)`

C

`A(z)=A(x)+A(y)`

D

`A(z)=A(x) [A(y)]^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
A
`A(x)A(y)=(1-x)^(-1) (1-y)^(-1)[(1,-x),(-x,1)][(1,-y),(-y,1)]`
`=(1+xy-(x+y))^(-1) [(,),(,)]`
`=(1- (x+y)/(1+xy))^(-1) [(1+xy,-(x+y)),(-(x+y),1+xy)]=A(z)`
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