Finding a matrix of an odd determinant I am trying to find a square matrix of size $n$ consisting of zeros and ones whose determinant is an odd number. Any ideas?
All identity matrices have determinant $1$.
More generally, all permutation matrices have determinant $\pm1$, and remember that adding a multiple of any row to any other row does not change the determinant. This should already give you many, many examples.
Another example (not in the instances described above) of a zero-one matrix with odd determinant is a $2n×2n$ matrix with zeros on the diagonal and ones elswehere – this has determinant $1-2n$.
Finally, the most general way of constructing a zero-one matrix with odd determinant is to take any integral matrix with odd determinant and reduce modulo $2$ (odds to $1$, evens to $0$), since $\mathbb Z_2$ is a field.
Also any diagonal matrix with odd elements on the diagonal, in fact:
$$\det(A)=a_{1,1}  \cdots a_{n,n}$$