Calculer \(A^k\) pour \(k \in \N\) :
1
\(A = \begin{pmatrix}1 & &(2)\cr &\ddots \cr (2)& &1 \cr\end{pmatrix}\).
2
\(A = \begin{pmatrix} 1 &2 &3 &4 \cr 0 &1 &2 &3 \cr 0 &0 &1 &2 \cr 0 &0 &0 &1 \cr \end{pmatrix}\).
3
\(A = \begin{pmatrix} x^2 &xy &xz \cr xy &y^2 &yz \cr xz &yz &z^2 \cr \end{pmatrix}\).