Binary matrix combinatorics

Hello,

the problem is to count how many $\displaystyle n \times n$ binary matrices there are with following properties

i. every column must have even number of $\displaystyle 1$'s

ii. every row must have even number of $\displaystyle 1$'s

For $\displaystyle 1 \times 1$ matrices there is none. For $\displaystyle 2 \times 2$ matrices there is one:

$\displaystyle \left(\begin{array}{cc}1&1\\1&1\end{array}\right)$

I think for 3x3 there isn't any. Atleast I couldn't construct one, but I suck at Sudoku's.

The number of square $\displaystyle n \times n$ binary matrices is calculated with $\displaystyle 2^{n^2}{$. So, I though maybe substracting the matrices without even number of $\displaystyle 1$'s from that number would help, but then we come the problem, how to pick out the correct matrices.

Any help is appreciated. Thank you!