Let $A\in\mathbb{R}^{n\times n}$ be Hurwitz. Let $k_1,k_2>0$. Consider the matrix
$$ M = \begin{bmatrix} 0 & I\\ k_1 A & k_2 A \end{bmatrix}, $$
where $0$ and $I$ denote respectively the zero matrix and the identity matrix in $\mathbb{R}^{n\times n}$.
1) Is $M$ also Hurwitz for any $k_1,k_2>0$?
2) If not, is there some necessary and/or sufficient condition on $k_1$ and $k_2$ for $M$ to be Hurwitz?
Edit: fixed a wrong sign