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We denote by $k$ a field of characteristic zero satisfying $H^1(k,\mathrm{Aut}(S{L}_2\left)\right)\ne 0$. Let $G$ be a connected $k$-split linear algebraic group acting on $X={\mathrm{Aff}}^n$ rationally by $\rho$ with a Zariski-dense $G$-orbit $Y$. A prehomogeneous vector space $(G,\rho$,X) is called “universally transitive” if the set of $k$-rational points $Y\left(k\right)$ is a single $\rho$ $\left(G\right)\left(k\right)$-orbit for all such $k$. Such prehomogeneous vector spaces are classified by J. Igusa when $\rho$ is irreducible. We classify them when $G$ is reductive and its commutator subgroup $[G,G]$ is either a simple algebraic...