Let M denote the set of all real matrices of order 3 × 3 and let S ={-3,-2,-1,1,2}. Let S_1={ A =[a_ij ] ∈ M: A = A^T. and.a_ij ∈ S, ∀ i, j }, S_2={…

Let M denote the set of all real matrices of order $\displaystyle 3 \times 3$ and let $\displaystyle \mathrm{S}=\{-3,-2,-1,1,2\}$. Let $\displaystyle \mathrm{S}_1=\left\{\mathrm{A}=\left[a_{\mathrm{ij}}\right] \in \mathrm{M}: \mathrm{A}=\mathrm{A}^{\mathrm{T}}\right.$ and $\displaystyle \left.a_{\mathrm{ij}} \in \mathrm{S}, \forall \mathrm{i}, \mathrm{j}\right\}$, $\displaystyle \mathrm{S}_2=\left\{\mathrm{A}=\left[a_{\mathrm{ij}}\right] \in \mathrm{M}: \mathrm{A}=-\mathrm{A}^{\mathrm{T}}\right.$ and $\displaystyle \left.a_{\mathrm{ij}} \in \mathrm{S}, \forall \mathrm{i}, \mathrm{j}\right\}$, $\displaystyle \mathrm{S}_3=\left\{\mathrm{A}=\left[a_{\mathrm{ij}}\right] \in \mathrm{M}: a_{11}+a_{22}+a_{33}=0\right.$ and $\displaystyle \left.a_{\mathrm{ij}} \in \mathrm{S}, \forall \mathrm{i}, \mathrm{j}\right\}$. If $\displaystyle \mathrm{n}\left(\mathrm{S}_1 \cup \mathrm{S}_2 \cup \mathrm{S}_3\right)=125 \alpha$, then $\displaystyle \alpha$ equls $\displaystyle \_\_\_\_$.