Two mathematical techniques - scalarization and symbolic technique - are promoted as useful techniques for the solution of dyadic differential equations. Both are employed to find a complete, analytic inversion of the dyadic differential operator × x I - a2I - b × I. An operator of this structure arises in the electromagnetic theory of isotropic chiral media. While describing the identical physical process, different mathematical formulations of chiral media have been put forward in the literature. The operator (and therefore the dyadic Green's function) analyzed here is the most general one that contains the other descriptions as special cases of the parameters.