Example2.2 Let \begin{equation*} A=\begin{pmatrix} 0 \amp 1 \amp 1 \amp 1\\ 0 \amp 0 \amp 1 \amp 1\\ 0 \amp 0 \amp 0 \amp 1\\ 0 \amp 0 \amp 0 \amp 0 \end{pmatrix}. \end{equation*} Write down \(A^2\text{,}\) \(A^3\) and \(A^4\text{.}\)