Given a matrix $A_{n \times n}$, which has elements $a_{i,j} \sim \mathrm{unif} \left[a,b\right]$, what is the probablity of $\det(A)$ being zero? What if $a_{i,j}$ have any other distribution?
Added: Let's assume an extension of the about problem; What is the probability of, $\mathbb{P}(|\det(A)| < \epsilon ), \; s.t. \; \epsilon \in \mathbb{R} $ ?
Thanks!