Question

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`

Answer 1

Correct Answer - 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)`