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**1. Homework Statement**

A square(nxn) matrix is called nilpotent of index k if A[tex]\neq[/tex]0, A^2[tex]\neq[/tex]0,....A^(k-1)[tex]\neq[/tex]0, But A^k=0 for some positive integer K

Verify that A={{{021,002,000}}} is nilpotent. What is its index? Show that for this matrix (I-A)-1= I + A + A^2

**3. The Attempt at a Solution**

I am unsure how different values of k affects the matrix... but For the equation (I-A)-1= I + A + A^2, I found the inverse of (I-A) which was {{{125,012,001}}}, which then gave me A^2 as {{{004,000,001}}}.

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