JEE Main 2022 · 28 Jun · Shift 2, Mathematics question 27

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