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 (BT xA)X = C.