if `A=[[i,0] , [0,i]]` where `i=sqrt(-1)` and `x epsilon N` then `A^(4x)` equals to:

Explanation

To solve the problem, we need to find \( A^{4x} \) where \( A = \begin{pmatrix} i & 0 \\ 0 & i \end{pmatrix} \) and \( i = \sqrt{-1} \).

### Step 1: Calculate \( A^2 \)

First, we will compute \( A^2 \):

\[
A^2 = A \cdot A = \begin{pmatrix} i & 0 \\ 0 & i \end{pmatrix} \cdot \begin{pmatrix} i & 0 \\ 0 & i \end{pmatrix}
...