In a recent article Matsubara-Heo and Telen introduced the theory of principle matroid determinants, which parallels the wellstudied concept of principle A-determinants by Gelfand, Kapranov and Zelevinsky. The presented work aims to answer several questions that were left open in this framework, but are known in the classical version of the theory. We identify the conormal varieties of reciprocal linear spaces as a central object in these questions and study their multidegrees. The tropicalisation of the reciprocal conormal variety is shown to be set-theoretically equal to the so called conormal fan of the underlying matroid, a combinatorial object that has been used by Ardila, Denham and Huh to prove several logconcavity conjectures in matroid theory. In this way our work gives a concrete geometric meaning to these combinatorial models in the realisable case.