How to find the conditional expectation $\mathbb{E}[A|b]$ of a multivariate normal pair $(A,B)\sim \mathcal{N}$?

Question

Suppose that $A,B$ are random Euclidean vectors and $(A,B)$ follows a multivariate normal distribution $$\mathcal{N}\left(\begin{bmatrix}E\\ F\end{bmatrix}, \begin{bmatrix}P & Q\\ R & S\end{bmatrix}\right)$$ how can we find the conditional expectation $\mathbb{E}[A|b]$