Given the matrix $A$ such that $A^3=0$. Determine if matrix $A^2-A+I$ is invertible, and if it is, find it's inverse.
Is it possible to directly evaluate matrix $A$ from the condition $A^3=0$? If not, can we use Cayley-Hamilton theorem?
Given the matrix $A$ such that $A^3=0$. Determine if matrix $A^2-A+I$ is invertible, and if it is, find it's inverse.
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linear-algebra
inverse
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0Duplicate.. see the third highly upvoted answer in my profile. – 2017-02-10
1 Answers
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($A+I$)($A^2$-$A$+$I$)=$I$
So that is invertible.