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.