Wehave performed ab initio calculations for the cubic inverse-perovskite Sc₃EN(E=Al,Ga,In) systems to study their electronic band-structures and elastic properties.In this study, we used the accurate augmented plane waveplus local orbital method to find the equilibrium structural parametersand to compute the full elastic tensors. The obtained single-crystalelastic constants were used to quantify the stiffness of theSc-based ternary nitrides and to appraise their mechanical stability. Thesite-projected density of states, Fermi surfaces, and the charge-density plotshave also been used to analyze the chemical bonding betweenthe Sc₆N cluster and the surrounding metallic lattice of eitherAl, Ga, or In atoms. Our calculations show that Sc₃GaNhas the largest covalent Sc-N bonding-type character with the highestYoung, shear, and bulk moduli. Compared with the other twoisoelectronic systems, it also behaves as the most brittle materialwith a relatively large elastic anisotropy.