matrices;
for 7, because there is only two variables, a and b, you only need to look at how many goats they both retain out of their current number
option A is the only one where location A keeps more goats than location B, but your method works perfectly too
for 8, in hindsight your way was probably quicker, but i did it by finding the inverse; 1/(ad-bc)=1/(-9+4k) and the matrix is -3 -k on the top and 4 3 on the bot
and then from looking at the original matrix and the half determined inverse one you can tell that 1/(-9+4k) has to equal -1 , so k=2
for 9, you have A=3x3, B=six elements, and AB is defined
columns in first has to equal rows in second so B has to have 3 rows
6 elements, 3 rows means 2 columns
if none of those are zero, you can, in this question just assume 1 for all of the values
and then you can just try putting the two defined numbers in the same row and different rows (in matrix A), and find the product with the least 0's
though im pretty sure my way of doing 9 is slow and stupid, some intelligent world leader to be would have a quicker answer than mine