Olympiad problems

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Found problems: 1

2025 VJIMC, 4

Tags: linear algebra , matrix , algebra , polynomial , trace , minimal polynomial

Let $A$ be an $n\times n$ real matrix with minimal polynomial $x^n + x - 1$. Prove that the trace of $(nA^{n-1} + I)^{-1}A^{n-2}$ is zero.