For my homework assignment, I'm supposed to find a basis for the space of 3x3 matrices that have zero row sums and separately for zero row columns. I am having a hard time with this as it seems to me that there are a lot of combinations I have to consider. For the first, it seems like the rows would have to consist of one 0, one 1, and one -1 in different orders... Is there a better way to do this other than brute force?