Laser-ablated Rh atoms react with H-2 to give RhH2 and RhH as primary products, which are trapped or react with additional hydrogen in the condensing solid argon, neon, and deuterium matrixes. RhH gives a major 1920.6 cm(-1) band in argon, a minor 1935.5 cm(-1) band in neon, and no absorption in deuterium. RhH2 produces sharp 2099.4 and 2053.4 cm(-1) and 2099.7 and 2052.2 cm(-1) bands in solid argon and neon, respectively and no absorption in deuterium; these absorptions increase on annealing the matrix to allow diffusion, which shows that ground state Rh inserts spontaneously into H-2. Additional absorptions at 2122.4 and 2078.2 cm(-1) (1527.3 and 1494.4 cm(-1) with D-2) in neon and at 1521.1 and 1496.1 cm(-1) in deuterium are assigned to the higher hydride complexes (H-2)RhH3 and (H-2)PhH2, respectively. A weaker 737.6 cm(-1) absorption in neon is due to the side-bound complex Rh(H-2)(2). Both (D-2)RhH2 and Rh(H-2)(D-2) rearrange H and D on photoexcitation suggesting a tetrahedral transition state. Rhombic (RhH)(2) is observed in all three matrix systems. These assignments are supported by D-2, HD, and H-2 + D-2 substitution and density functional theory frequency and structure calculations.