Let $G$ be the $d-regular\ graph$ and $A$ be an incident matrix of $G$. Also Suppose $B$ is a reduced echelon form of $A$ such that computations are in $\mathbb F_2$. With matrix $B$, can we find matrix $A$?

If yes,how we can? and for arbitrary sparse matrix $A$ is this true?

And if no, can we use this method for constructing hash function?

Let $G$ be a $d$-regular graph, and $A$ be the incidence matrix of $G$. Also suppose $B$ is a reduced echelon form of $A$ such that computations are in $\mathbb F_2$. Given matrix $B$, can we find matrix $A$?

If yes, how? and for arbitrary sparse matrix $A$ is this true?

And if no, can we use this method for constructing hash function?