Maybe you can find first how many symmetric 2 x 2 and 3 x 3 (0, 1)-matrices there are.
I hope this is what you mean.
How many 6x6 matrices can be there such that . Elements of the matrices can be selected from the set ?
Sol: For we need where is the element in the row column.
We consider the elements where (why ?). There are 21 such elements and for each of these elements we have 2 choices so we have such matrices.
Kalyan.