  Multiferroics are compounds in which at least two ferroic orders coexist -
typically (anti)ferromagnetism and ferroelectricity. While magnetic order can
arise in both insulating and conducting compounds, ferroelectricity is in
principle not allowed in metals although a few two-dimensional (semi)metals
were reported to behave as ferroelectrics. Yet, the combination with magnetic
order to realize multiferroic metals remains elusive. Here, by combining x-ray
spectroscopy and magnetotransport, we show the coexistence of ferroelectricity
and magnetism in an oxide-based two-dimensional electron gas (2DEG). The data
evidence a non-volatile switching of the polar displacements and of the
anomalous Hall effect by the polarization direction, demonstrating a
magnetoelectric coupling. Our findings provide new opportunities in quantum
matter stemming from the interplay between ferroelectricity, ferromagnetism and
Rashba spin-orbit coupling in a 2DEG.
