Catalyzes the conversion of glucosamine-6-phosphate to glucosamine-1-phosphate. Can also catalyze the formation of glucose-6-P from glucose-1-P, although at a 1400-fold lower rate. alpha-D-glucosamine 1-phosphate = D-glucosamine 6-phosphate Binds 1 Mg(2+) ion per subunit. Autophosphorylation is inhibited by inorganic phosphate or EDTA. Activated by phosphorylation. Can autophosphorylate in vitro using ATP, alpha-D-glucosamine 1,6-bisphosphate or alpha-D-glucose 1,6-bisphosphate. Catalysis proceeds by a classical ping-pong bi-bi reaction mechanism, with alpha-D-glucosamine 1,6-bisphosphate as an intermediate. Belongs to the phosphohexose mutase family.