Cramer’s rules for the system of quaternion matrix equations with η-Hermicity

The system of two-sided quaternion matrix equations with η-Hermicity, A1XA1η* = C1, A2XA2η* = C2 is considered in the paper. Using noncommutative row-column determinants previously introduced by the author, determinantal representations (analogs of Cramer’s rule) of a general solution to the system are obtained. As special cases, Cramer’s rules for an η-Hermitian solution when C1 = Cη*1 and C2 = Cη*2 and for an η-skew-Hermitian solution when C1 = −Cη*1 and C2 = −Cη*2 are also explored.