In this paper we obtain a general solution of the Penrose's equation (3), solution of the equation (4) and a general solution of the system of Penrose's equations (1),(3) and (1),(4). We also introduce a determinantal representation of the classes of $\{3\}$, $\{4\}$, $\{1,3\}$ and $\{1,4\}$-inverses of complex matrices.