Computing a few Invertible matrices

Problem: Enumerate and generate the number of invertible matrices (n*n) with each entry either 0 or 1.

Example: For n=2, we have a set of 6 matrices. They are

Interestingly, these matrices form a group under matrix multiplication.

A much more harder problem would be to enumerate and generate all invertible (n*n) matrices with enrites fron the set { 0,1,...,n-1 }.