Let the bivariate random variable $A=(A_1,A_2)^T$ have a Gaussian distribution on $\mathbb{R}^2$ with zero mean and covariance matrix be given by
$$\begin{pmatrix} 1 & -0.4\\-0.4 & 1\end{pmatrix}$$.
Let $B$ = $\begin{pmatrix} 1 \\ 2 \end{pmatrix}$ and $C$= $\begin{pmatrix} 2 \\ 1 \end{pmatrix}$. Define $X=B^TA,Y=C^TA$. How do I find the covariance of X and Y?
I know that $cov(X,Y) = E(XY)-E(X)E(Y)$. I don't quite understand how to read a covariance matrix.