So Let matrix $A$ have eigenvalues as follows :

$$
e\_1=0\\
e\_2=0\\
e\_3=2\\
e\_4=2\\
$$

From here can we deduce that dimension of the eigenspace when the eigenvalues is $2$ is 2? can we deduce this? 

If we could deduce that we could also deduce that dimension of the nullspace is $2$ since $e\_1=e\_2=0$ two eigenvalues pointing at $0$

To clear the question a bit :

Can we conclude that rank of the eigenspace of a specific eigenvalue is equal the number of repetition of the eigenvalue?