Let $\displaystyle M$ be a $\displaystyle (0, 1)$ matrix; that is, a matrix where each of whose entries is either a 0 or a 1. A line in $\displaystyle M$ is either a row or a column of $\displaystyle M$. Use Konig's theroem to prove that the minimum number of lines containing all the 1's of $\displaystyle M$ is equal to the maximum number of 1's, no two of which are in the same line.

My attempt:

Let $\displaystyle G$ be a bipartite graph with vertex bipartition $\displaystyle {X, Y}$ , such that $\displaystyle A$ is an adjacency matrix of graph $\displaystyle G$, where $\displaystyle X$ is a set of vertices corresponding to the rows of matrix $\displaystyle A$, and $\displaystyle Y$ is the vertex set corresponding to the columns. So the result follows from Konig's thereom. I am not sure how the adjacency matrix helps for making this bipartition. I would like some help on this one. Thanks in advance.