Catalyzes the NAD(P)H-dependent reduction of dihydroxyacetonephosphate (DHAP or glycerone phosphate) to glycerol 1-phosphate (G1P). The G1P thus generated is used as the glycerophosphate backbone of phospholipids in the cellular membranes of Archaea. NAD(+) + sn-glycerol 1-phosphate = dihydroxyacetone phosphate + H(+) + NADH NADP(+) + sn-glycerol 1-phosphate = dihydroxyacetone phosphate + H(+) + NADPH Binds 1 zinc ion per subunit. Membrane lipid metabolism; glycerophospholipid metabolism. Homodimer. Belongs to the glycerol-1-phosphate dehydrogenase family.