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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
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The possible values of det A are -1, 0, and 1.

 Apr 4, 2021

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