MathNet 2024-part-04 — 168 problems (EN–VI) Question 127

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

Sorin Rădulescu and Mihai Piticari