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Easy problem about commutativity in division rings

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

April 3, 2024
division ringsabstract algebra

Problem Statement

Let (K,+,⋅)(\mathbb{K},+, \cdot) be a division ring in which x2y=yx2,x^2y=yx^2, for all x,y∈K.x,y \in \mathbb{K}. Prove that (K,+,⋅)(\mathbb{K},+, \cdot) is commutative.
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