matrices

the matrices in this question have elements from the set {0,1,2,...,n}

(i) what's the probability a 2x2 matrix has determinant 0?

(ii) now consider an mxm matrix, which precisely p zero elements. what's the probability its determinant is zero?

Sequence of the number of 2x2 matrices, elements 0..n, with determinant 0.

http://www.research.att.com/~njas/sequences/A059306