Multiple choice questions can be answered by trial and error.
Let's use the squares 1 and 9 which are "perfect odd squares". Form the
determinant
9 1 1
1 9 1
1 1 9
and evaluate. I get the determinant is 704, which factors to 64 x 11. That eliminates all but choices 'a' and 'c'. Certainly if the determinant is a multiple of 16 it is also a multiple of 4. So 'a' seems safe.
Clearly this isn't a proof and assumes the problem relies on a true fact.