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# Nilpotent matrices

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A matrix A is said to be nilpotent if $$\mathbf A^k = \mathbf 0$$ for some positive integer k. What are the possible values of $$\det \mathbf A?$$

Here's what I have so far: I know that one matrix that is nilpotent is $$\begin{pmatrix} 0 & 0 \\ 1 & 0 \end{pmatrix}$$, where the determinant would be -1. I tried plugging in different numbers where 1 was and raising that matrix to different powers and I got the zero matrix for every number I tried. Does this mean that there are infinitely many solutions? Thanks!

Mar 20, 2021