Covariance matrix of two i.i.d. Gaussian random variables

Question

I have two i.i.d. Gaussian random variables:

$$Z_a - \mathcal N(0,N_a)$$ $$Z_b - \mathcal N(0,N_b)$$

I am trying to construct the covariance matrix of $(Z_a,Z_b)$.

I guess it should be something like: $$(0,\begin{bmatrix} N_aN_b & pN_aN_b \\ pN_aN_b & N_aN_b \\ \end{bmatrix})$$

But it appears that it is not.