I'm am taking a particular random vector that converges in distribution to a MVN(0,sigma). I am left, from using the central limit theorem, with a sqrt(n) on the left side. I believe that I need to prove that the covariance matrix is non-degenerate before I can move the sqrt(n) over into the expression of the MVN. Is there an easy way to do this (or what do I need to do in order to show this)? The covariance matrix is a multinomial matrix with n =1 and I know that all values of p add up to 1. I thus seem to have enough equations to determine this?