We assume that $k \geqslant 0$ and that $C$ is a matrix in $\Delta_{k+1}$. We set $P = I_n + C$. Show that $P$ is invertible and that $P^{-1} \in \bigoplus_{p=0}^{n-1} \Delta_{p(k+1)}$.
We assume that $k \geqslant 0$ and that $C$ is a matrix in $\Delta_{k+1}$. We set $P = I_n + C$. Show that $P$ is invertible and that $P^{-1} \in \bigoplus_{p=0}^{n-1} \Delta_{p(k+1)}$.