JEE Math Practice Question

Let S = {$$\sqrt{n}$$ : 1 $$\le$$ n $$\le$$ 50 and n is odd}. Let a $$\in$$ S and $$A = \left[ {\begin{matrix} 1 & 0 & a \\ { - 1} & 1 & 0 \\ { - a} & 0 & 1 \\ \end{matrix} } \right]$$. If $$\sum\limits_{a\, \in \,S}^{} {\det (adj\,A) = 100\lambda } $$, then $$\lambda$$ is equal to :

1. A.218
2. B.221
3. C.663
4. D.1717