If A is a 3 ×3 matrix and 5(A+I)=I. What is det(A+I) .

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asked Apr 24, 2018 46.7k views

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If A is a 3 ×3 matrix and 5(A+I)=I. What is det(A+I) .

Mathematics
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Vullnet asked

by Vullnet

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$5(\mathbf A+\mathbf I)=\mathbf I\implies \mathbf A=-\frac45\mathbf I$

$\implies\det\mathbf A=\det\left(-\frac45\mathbf I\right)=\left(-\frac45\right)^3\det\mathbf I=-(64)/(125)$

Nielk answered Apr 29, 2018

by Nielk

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