We consider the matrix $K \in \mathscr{M}_N(\mathbf{R})$ defined by
$$\forall (i,j) \in \llbracket 1;N \rrbracket^2, K[i,j] = p_{ij}$$
where $p_{ij}$ is the probability of moving from state $i$ to state $j$ at each impulse. Justify that $K$ is a Markov kernel.