  In this paper properties of the determinant of a Hermitian matrix are
investigated, and determinantal representations of the inverse of a Hermitian
coquaternionic matrix are given. By their using, Cramer's rules for left and
right systems of linear equations with Hermitian coquaternionic matrices of
coefficients are obtained. Cramer's rule for a two-sided coquaternionic matrix
equation ${\bf AXB}={\bf D}$ (with Hermitian ${\bf A}$, ${\bf B}$) is given as
well.
