If $A =\begin{bmatrix}i&0\\0&i\end{bmatrix},n∈N$, then $A^{4n}$ equals
Answer & explanation
Correct answer: option 3
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
$A^{4n}=\begin{bmatrix}i^{4n}&0\\0&i^{4n}\end{bmatrix}=\begin{bmatrix}1&0\\0&1\end{bmatrix}$