Thank you, that generates the equations perfectly!  Is there a trick to get them to work with the solve command?  I tried

solve({eqs}, {a[1, 1], a[1, 2], a[2, 1], a[2, 2]});

but got an error that said "Invalid input."  Thanks again, you have been extrmely helpful.

Yes, the example was rather silly - in reality I'll be dealing with the determinant of sums of matricies being equal to zero.  Is there a way to implement something like a for loop so that I don't have to type in the equation of each entry manually?  It seems very inefficient to have to type out n^2 equations by hand when I'm really just saying that A^2=A.  Thanks for your help!