Real Analysis: What does it mean for the set of invertible nxn matrices to be open? 1. The problem statement, all variables and given/known data The set of invertible nxn matrices is open in M, is it also dense? 2. The attempt at a solution Let S = set of invertible nxn matrics, S contained in M Let A be any invertible element in S. We want to show that there exists an open ball of ivertible elements centered at A. Let 0 < d < det^-1(A) But I have ho idea what it means for the set of invertible nxn matrices to be open or how to proceed from here. Any help would be great!