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Romania NMO 2022 Grade 11 P4

Source: Romania National Olympiad 2022

April 20, 2022
linear algebraMatricesromania

Problem Statement

Let A,B∈Mn(C)A,B\in\mathcal{M}_n(\mathbb{C}) such that A2+B2=2AB.A^2+B^2=2AB. Prove that for any complex number xxdet⁡(A−xIn)=det⁡(B−xIn).\det(A-xI_n)=\det(B-xI_n).Mihai Opincariu and Vasile Pop
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