TITLE: Characterizing invertible matrices with {0,1} entries
QUESTION [8 upvotes]: Related to the question link text I was asking myself some time ago the following. Can one precisely describe the invertible n\times n matrices with{0, 1} entries? For example, is anything special about the graph asociated to this matrix?

REPLY [3 votes]: At least for symmetric matrices, such graphs have been studied under the name singular graphs. See, for instance, this paper.