If $A = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$, then $A^2$ is equal to

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

The correct answer is Option (4) → $\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ ##

$∵A^2 = A \cdot A = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} = \begin{bmatrix} 0+1 & 0+0 \\ 0+0 & 1+0 \end{bmatrix} = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$