Problem

Source: Romanian National Olympiad 2024 - Grade 12 - Problem 2

Tags: division rings, abstract algebra



Let $(\mathbb{K},+, \cdot)$ be a division ring in which $x^2y=yx^2,$ for all $x,y \in \mathbb{K}.$ Prove that $(\mathbb{K},+, \cdot)$ is commutative.