Find the matrix $A^2$, where $A = [a_{ij}]$ is a $2 \times 2$ matrix whose elements are given by $a_{ij} = \text{maximum} (i, j) - \text{minimum} (i, j) :$ (A) $\begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}$ (B) $\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$ (C) $\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ (D) $\begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix}$