In $\mathrm{Sp}(2)$, a loop of degree zero moves $e_1$ along a null-homotopic loop in $\mathbb R^2\setminus\{0\}$

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In $\mathrm{Sp}(2)$, a loop of degree zero moves $e_1$ along a null-homotopic loop in $\mathbb R^2\setminus\{0\}$ · Prove2Me