Singleton_is_Linearly_Independent

Let $K$ be a division ring. Let $\struct {G, +_G}$ be a group whose identity is $e$. Let $\struct {G, +_G, \circ}_K$ be a $K$-vector space whose zero is $0_K$. Let $x \in G: x \ne e$. Then $\set x$ is a linearly independent subset of $G$.