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A new phenomenon, overlooked for decades, here called AKAF, was recently discussed by several groups. It represent a fully compensated antiferromagnet with no net magnetization, which nonetheless manifests time-reversal symmetry breaking typical of ferromagnets: exchange band splitting, anomalous Hall effect (AHE), and magneto-optical Kerr effect (MOKE). In this talk we concentrate on a well known semiconductor, FeSb₂, and show several highly unexpected features: (1) DFT ground state is not paramagnetic, and not, as suggested by some, ferro-, but antiferromagnetic (AF); (2) two different AF exist, and the most stable one corresponds to the so-called AFMe order, observed experimentally in CrSb₂ (which is NOT AKAF); (3) the energetically favorable AKAF state is metallic, and the nonmagnetic one semiconducting, which is highly unusual; (4) the AFMe order is preferential to the AKAF one, since it has a pseudogap at E_F. and the paramagnetic one is realized in nature because of the gap opening; (5) doping with Cr or Co reduces the advantage of (pseudo-)gapping, and in a narrow range of doping the AKAF becomes the ground state. We calculate AHE and MOKE, which appear nonzero for two magnetization directions, including the DFT easy axis.