Let $A \in \mathscr{M}_{N}(\mathbf{R})$. Show that $A$ satisfies $(M_2)$ if and only if $AU = U$. Deduce that if $A$ and $B$ are two Markov kernels then $AB$ is also a Markov kernel.
Let $A \in \mathscr{M}_{N}(\mathbf{R})$. Show that $A$ satisfies $(M_2)$ if and only if $AU = U$.\\
Deduce that if $A$ and $B$ are two Markov kernels then $AB$ is also a Markov kernel.