Let f(x)=(1+x)/(1-x) . If A is matrix fo...

Let `f(x)=(1+x)/(1-x)` . If `A` is matrix for which `A^3=O ,t h e nf(A)` is `I+A+A^2` b. `I+2A+2A^2` c. `I-A-A^2` d. none of these

A

`I+A+A^(2)`

B

`I+2A+2A^(2)`

C

`I-A-A^(2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:

B

`(I-A) f(A)=I+A`
or `f(A)=(I+A)(I-A)^(-1)`
`=(I+A)(I+A+A^(2))`
`=I+A+A^(2)+A+A^(2)+A^(3)`
`=I+2A+2A^(2)`

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