Find the matrix A^2, where A =[ a_ij ] is a 2 × 2 matrix whose elements are given by a_ij = maximum ( i, j ) - minimum ( i, j ):

Find the matrix $\displaystyle \mathrm{A}^{2}$, where $\displaystyle \mathrm{A}=\left[\mathrm{a}_{\mathrm{ij}}\right]$ is a $\displaystyle 2 \times 2$ matrix whose elements are given by $\displaystyle \mathrm{a}_{\mathrm{ij}}=$ maximum ( $\displaystyle \mathrm{i}, \mathrm{j}$ ) - minimum ( $\displaystyle \mathrm{i}, \mathrm{j}$ ) :