If matrix 𝐴 = $$\begin{bmatrix} 2 & 2 \\ 0 & 2 \end{bmatrix}\text{ and } A^2 = \begin{bmatrix} 4 & x \\ 0 & 4 \end{bmatrix}$$, then the value of x is :

$$\phantom{\Rightarrow} A^2 = \begin{bmatrix} 2 & 2 \\ 0 & 2 \end{bmatrix}\begin{bmatrix} 2 & 2 \\ 0 & 2 \end{bmatrix} \\[1em] \Rightarrow A^2 = \begin{bmatrix} 2 \times 2 + 2\times 0 & 2 \times 2 + 2 \times 2 \\ 0 \times 2 + 2 \times 0 & 0 \times 2 + 2 \times 2 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix} 4 & x \\ 0 & 4 \end{bmatrix} = \begin{bmatrix} 4 + 0 & 4 + 4 \\ 0 + 0 & 0 + 4 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix} 4 & x \\ 0 & 4 \end{bmatrix} = \begin{bmatrix} 4 & 8 \\ 0 & 4 \end{bmatrix} \\[1em] \Rightarrow x = 8.$$

Hence, Option 3 is the correct option.