Matrices and Determinants

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