Find the matrix \({\mathrm{A}}^{2}\), where \(\mathrm{A}=\left[{\mathrm{a}}_{\mathrm{ij}}\right]\) is a \(2\times 2\) ma…

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