The MO configuration of O−2 is KK(σ2s)2(σ∗2s)2(σ2px)2(π2py)2(π2pz)2(π∗2py)2(π∗2pz)1
The MO configuration of O2−2 is KK(σ2s)2(σ∗2s)2(σ2px)2(π2py)2(π2pz)2(π∗2py)2(π∗2pz)2
The electronic configuration of O2− is 1s22s22p2x2p2y2p2z
Thus, KO2 is paramagnetic (with one unpaired electron in O−2) while K2OandK2O2 are diamagnetic.
Hence, the given statement is false.