Denote by a finite dimensional central algebra over a field with an involution (char), and by the set of all -matrices over . For set , , . is called (skew)selfconjugate if (if ), per(skew)selfconjugate if (if ), centro(skew)symmetric if (if ). Any two of these three properties imply the third one. is bi(skew)symmetric if it is (skew)selfconjugate and per(skew)selfconjugate at the same time.
The paper treats the following system of matrix equations over , , . Necessary and sufficient conditions are given for the existence of bi(skew)symmetric solutions to and over and of solutions to where is bisymmetric (biskewsymmetric) and is biskewsymmetric (bisymmetric). Auxiliary results dealing with systems of Sylvester equations or are also presented.