Show that there not exists $A\in Gl_{2n+1}(\mathbb{C})$ s.t. $$A^2+A^{-1}+I_{2n+1}=O_{2n+1}.$$
My first attempt was to use the minimal polynomial. It should divide $x^3+x+1$.
2026-03-30 17:00:16.1774890016
$A^2+A^{-1}+I_{2n+1}=O_{2n+1}.$
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