The nature of the magnetic transition of the Na-rich thermoelectric Na$_{0.75}$CoO$_2$ at 22K was studied by positive muon-spin-rotation and relaxation ($mu^+$SR) spectroscopy, using a polycrystalline sample in the temperature range between 300 and 2.5 K. Zero field $mu$SR measurements indicated the existence of a static internal magnetic field at temperatures below 22 K (= $T_{rm m}$). The observed muon spin precession signal below $T_{rm m}$ consisted of three components with different precession frequencies, corresponding to three inequivalent muon$^+$ sites in the Na$_{0.75}$CoO$_2$ lattice. The total volume fraction of the three components was estimated as $sim$21% at 2.5 K; thus, this magnetic transition was not induced by impurities but is an intrinsic change in the magnetism of the sample, although the sample was magnetically inhomogeneous otherwise. On the other hand, a similar experiment on a Na$_{0.65}$CoO$_2$ sample exhibited no magnetic transition down to 2.5 K; which indicates that the average valence of the Co ions is responsible for inducing the magnetic transition at 22 K.
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