Let $\mathrm{S}=\left\{\left(\begin{array}{cc}-1 & \mathrm{a} \\ 0 & \mathrm{~b}\end{array}\right) ; \mathrm{a}, \mathrm{b} \in\{1,2,3, \ldots 100\}\right\}$ and let $\mathrm{T}_{\mathrm{n}}=\left\{\mathrm{A} \in \mathrm{S}: \mathrm{A}^{\mathrm{n}(\mathrm{n}+1)}=\mathrm{I}\right\}$. Then the number of elements in $\bigcap_{\mathrm{n}=1}^{100} \mathrm{~T}_{\mathrm{n}}$ is $\_\_\_\_$ .