  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
$AXB=C$.
