Let $A_{n \times n} = (a_{ij}), n\geq 3,$ where $ a_{ij}=(b_i^2-b_j^2),i,j=1,2,\ldots,n$ for some distinct real numbers $b_1,b_2, \ldots, b_n.$ Then det$(A)$ is
(1)$\prod_{i<j}(b_i-b_j).$
(2) $\prod_{i<j}(b_i+b_j).$
(3) 0.
(4) 1.
We know that for odd number matrix is skew symmetric. Hence determinant is zero. Hence we can eliminate option (1) and (4). How to eliminate (2) option?
I think the question is asking which of the four expressions are always identical to $\det(A)$, otherwise you cannot really eliminate option 2, because it can be zero when $b_i=-b_j$ for some $i\ne j$.
Anyway, as $A=be^T-eb^T$ where $b=(b_1^2,b_2^2,\ldots,b_n^2)^T$, $A$ is a rank-two matrix. Hence $\det(A)=0$ when $n\ge3$.