Is this block matrix Hurwitz?

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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