  The reciprocal theorems of Maxwell and Betti are foundational in mechanics
but have so far been restricted to infinitesimal deformations in elastic
bodies. In this manuscript, we present a reciprocal theorem that relates
solutions of a specific class of large deformation boundary value problems for
incompressible bodies; these solutions are shown to identically satisfy the
Maxwell-Betti theorem. The theorem has several potential applications such as
development of alternative convenient experimental setups for the study of
material failure through bulk and interfacial cavitation, and leveraging easier
numerical implementation of equivalent auxiliary boundary value problems. The
following salient features of the theorem are noted: (i) it applies to dynamics
in addition to statics, (ii) it allows for large deformations, (iii) generic
body shapes with several potential holes, and (iv) any general type of boundary
conditions.
