On the Centro-symmetric Solution of a System of Matrix Equations over a Regular Ring with Identity

In this paper, we find the centro-symmetric solution of a system of matrix equations over an arbitrary regular ring with identity. We first derive some necessary and sufficient conditions for the existence and an explicit expression of the general solution of the system of matrix equations A1X1 = C1, A2X1 = C2, A3X2 = C3, A4X2 = C4 and A5X1B5 + A6X2B6 = C5 over . By using the above results, we establish two criteria for the existence and the representation of the general centro-symmetric solution of the system of matrix equations AaX = Ca, AbX = Cb and AcXBc = Cc over the ring .

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