In reply to Joseph Pingenot.

To complete the thought, the determinant is a single equation, which removes one variable from the set of equations. So (to first order) you have one variable (2^64 possible values) in 2^64^N possible values, or a 1 in 2^(64*(N-1)) chance of drawing a singular matrix (note that N is the number of matrix elements, which scales as V^2 with the number of variables. So the chance of drawing a random matrix scales inversely with the size of the matrix, by my reckoning.