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If A is an idempotent matrix satisfying ...

If `A` is an idempotent matrix satisfying `(I-0.4A)^(-1)=I-alphaA` where `I` is the unit matrix of the same order as that of `A` then the value of `alpha` is

A

`-1//3`

B

`1//3`

C

`-2//3`

D

`2//3`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` Given `A^(2)=A`
`impliesI=(I-0.4A)(I-alphaA)`
`=I-IalphaA-0.4AI+0.4alphaA^(2)`
`=I-Aalpha-0.4A+0.4alphaA`
`=I-A(0.4+alpha)+0.4alphaA`
`implies 0.4alpha=0.4+alpha`
`impliesalpha=-(3)/(2)`
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