Reproductive and non-reproductive solutions of the matrix equation AXB=C

In this article we consider a consistent matrix equation $AXB=C$ when a particular solution $X_0$ is given and we represent a new form of the general solution which contains both reproductive and non-reproductive solutions (it depends on the form of particular solution $X_0$). We also analyse the solutions of some matrix systems using the concept of reproductivity and we give a new form of the condition for the consistency of the matrix equation $AXB=C$.