Matrix Covariance Algebra

Question

In the structural equation modeling (SEM) context, one of the modeling frameworks is called the reticular action model (RAM). In RAM, the observed variables (y) and latent variables (η) are combined in one vector.

v = [y η](transpose of this matrix)

This can be modeled with an assymetric matrix A and a symmetric matrix S:

v = Av + u
u ∼ N(0,S)

I want to derive the var(v) in terms of A and S. Using matrix covariance algebra, I tried to do this:

var(Av + u)
cov(Av + u, Av + u)
cov(Av,Av + u) + cov(u,Av + u)
cov(Av,Av) + cov(Av,u) + cov(u,Av) + cov(u,u)

The last term is the variance of u, therefore equivalent to S, but I am unsure about the rest.