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If `A` is an idempotent matrix satisfying, `(I-0. 4 A)^(-1)=I-alphaA ,w h e r eI` is the unit matrix of the name order as that of `A ,` then th value of `|9alpha|` is equal to ________.

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The correct Answer is:
6
Given `A^(2)=A`
Now `I=(I-0.4A) (I-alphaA)`
`=I-IalphaA-0.4 AI+0.4 alpha A^(2)`
`=I-Aalpha-0.4A+0.4 alpha A`
`= I-A(0.4+alpha) + 0.4 alpha A`
`implies 0.4 alpha=0.4+alpha`
`implies alpha=-2//3`
`implies |9alpha|=6`
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