  We compute the equations and multidegrees of the biprojective variety that
parametrizes pairs of symmetric matrices that are inverse to each other. As a
consequence of our work, we provide an alternative proof for a result of
Manivel, Michalek, Monin, Seynnaeve and Vodi\v{c}ka that settles a previous
conjecture of Sturmfels and Uhler regarding the polynomiality of maximum
likelihood degree.
