How do I show that the entries in the bottom matrix do or do not add up to 2?
I think, because after grouping some terms you get (a+c)(e+f)(b+d)(g+h), that it will equal zero because if there are no negative numbers, the numbers have to be 2, 1, or 0. Since at least two of the entries have to be 0, the answer is a 1 or a 0, not 2
>>380514
>(a+c)(e+f)(b+d)(g+h)
How did you get that? I had tried
ae+bg+af+bh+ce+dg+cf+dh
a(e+f)+b(g+h)+c(e+f)+d(g+h)
(a+c)(e+f)+(b+d)(g+h)
And gotten here but that's not what you got. And I think there can be negative numbers.
>>380523
Oh, you right, thats the way to group them. Though, if we take it a step back, is there some way to use the fact that we've got a(e+f)+b(g+h)+c(e+f)+d(g+h) and know that a+b+c+d=2?
Oh, e+f =2-g-h
>>380528
Does subbing that in give the answer?