  We clarify the linear algebra used in the quaternionic pluripotential theory
so that proofs of several results there can be greatly simplified. In
particular, we characterize and normalize real $2$-forms with respect to the
quaternionic structure, and show that the Moore determinant of a quaternionic
hyperhermitian matrix is the coefficient of the exterior product of the
associated real $2$-form. As a corollary, the quaternionic Monge-Amp\`{e}re
operator is the coefficient of the exterior product of the Baston operator.
