Rank of a matrix with block matrices

Question

So, given $A\in M_{3{\times}4}(R)$ has rank $2$, I built a new matrix -

$M=\begin{pmatrix} A& 0& A\\ 0& A& 4A\\ 0& 0& 0 \end{pmatrix}$

Can I claim, that since the rank of $A$ is $2$, and the rows of $M$ are LI, the rank of $M$ is $4$?

Thanks