  This paper deals with necessary and sufficient condition for consistency of
the matrix equation $AXB = C$. We will be concerned with the minimal number of
free parameters in Penrose's formula $X = A^(1)CB^(1) + Y - A^(1)AYBB^(1)$ for
obtaining the general solution of the matrix equation and we will establish the
relation between the minimal number of free parameters and the ranks of the
matrices A and B. The solution is described in the terms of Rohde's general
form of the {1}-inverse of the matrices A and B. We will also use Kronecker
product to transform the matrix equation $AXB = C$ into the linear system $(B^T
\otimes A)vecX = vec C$.
