Application of Schur's Lemma

Question

Given three matrices , $B_1 \in Mat_{n_1}(k)$, $B_2 \in Mat_{n_2}(k)$, and $C \in Mat_{n_1 \times n_2}(k)$, where $k$ is a perfect field, and $B_1 $ and $B_2$ are irreducible matrices. Required to show that there exists a matrix $X$ such that $$C+B_1X-XB_2=0$$ The given hint is to use Schur's lemma, however I try hardly but till now no sensible proof I can construct, any help would be highly appreciated. NOTE: what I mean by an irreducible matrix, is that its representing a linear map $f$ on a finite dimensional vector space that has no proper $f$ invariant subspaces.