Let A be an n ? n matrix, whose entries are independent copies of a centered random variable satisfying the subgaussian tail estimate. We prove that the operator norm of A^{-1} does not exceed Cn^{3/2} with probability close to 1. In a geometric language, this bounds the probability that the affine span of n random vectors in \mathbb{R}^n with i.i.d. subgaussian coordinates comes close to the origin.