Ok, so this was assigned as a bonus problem in my Topology class a while ago. Nobody in the class got it, but I've still been racking my brain on it ever since. ____ For some n, consider the set of all nxn nonsingular matrices, and using the usual Euclidean topology on this space, show that: a) the inverse is a continuous function. f(A) -> A^(-1) b) matrix multiplication is a continuous function. g(A,B) -> AB __________ I've thought quite a bit about this problem, but I really don't know where to go. If I can show that the determinant is continuous, then I think I can do part a, since calculating the inverse is just equivalent to calculating a bunch of determinants (Cramer's rule). As for part b, I am lost.