If $A =\begin{bmatrix}i&0\\0&i\end{bmatrix},n∈N$, then $A^{4n}$ equals

$\begin{bmatrix}i&0\\0&i\end{bmatrix}$ $\begin{bmatrix}0&0\\0&0\end{bmatrix}$ $\begin{bmatrix}1&0\\0&1\end{bmatrix}$ $\begin{bmatrix}0&i\\i&0\end{bmatrix}$

$\begin{bmatrix}1&0\\0&1\end{bmatrix}$

We have, $A =\begin{bmatrix}i&0\\0&i\end{bmatrix}$ Clearly, A is a diagonal matrix. Therefore, $A^{4n}$ is also a diagonal matrix such that $A^{4n}=\begin{bmatrix}i^{4n}&0\\0&i^{4n}\end{bmatrix}=\begin{bmatrix}1&0\\0&1\end{bmatrix}$