Bivariate Normal Manipulation

Question

I do not understand the section of the solution highlighted.

Answer 1

$M$ is a transform matrix, $U$ and $V$ are random vectors.

$V = M U$

$E[V] = E[MU] = ME[U]$

$E[VV^T] = E[MU(MU)^T] = E[MU U^T M^T] = M E[UU^T] M^T$

Since the transformation is linear, so this is so call affine transform of R.Vs.