## Konig's Theorem, matrix

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

My attempt:

Let $G$ be a bipartite graph with vertex bipartition ${X, Y}$ , such that $A$ is an adjacency matrix of graph $G$, where $X$ is a set of vertices corresponding to the rows of matrix $A$, and $Y$ 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.