Let $\mathrm{A}=\left(\begin{array}{cc}1+\mathrm{i}& 1\\ -\mathrm{i}& 0\end{array}\right)$ where $\mathrm{i}=\sqrt{-1}$. Then, the number of elements in the set $\left\{\mathrm{n}\in \{1,2,\dots \dots ,100\}:{\mathrm{A}}^{\mathrm{n}}=\mathrm{A}\right\}$ is _________.

$\begin{array}{l}\mathrm{A}=\left[\begin{array}{cc}1+\mathrm{i}& 1\\ -\mathrm{i}& 0\end{array}\right]\\ {\mathrm{A}}^2=\left[\begin{array}{cc}1+\mathrm{i}& 1\\ -\mathrm{i}& 0\end{array}\right]\left[\begin{array}{cc}1+\mathrm{i}& 1\\ -\mathrm{i}& 0\end{array}\right]\\ {\mathrm{A}}^2=\left[\begin{array}{cc}\mathrm{i}& 1+\mathrm{i}\\ -\mathrm{i}+1& -\mathrm{i}\end{array}\right]\\ {\mathrm{A}}^4=\left[\begin{array}{cc}\mathrm{i}& 1+\mathrm{i}\\ -\mathrm{i}+1& -\mathrm{i}\end{array}\right]\left[\begin{array}{cc}\mathrm{i}& 1+\mathrm{i}\\ -\mathrm{i}+1& -\mathrm{i}\end{array}\right]\\ {\mathrm{A}}^4=\left[\begin{array}{ll}1& 0\\ 0& 1\end{array}\right]=\mathrm{I}\\ {\mathrm{A}}^{4\mathrm{n}+1}=\mathrm{A}\\ \mathrm{n}=1,5,9,\dots \dots ,97\\ \Rightarrow \text{ total elements in the set is }25.\end{array}$