Extract a matrix of the expected value.

Question

Let $Y$~$N(\mu, V)$ be a random vector $p$x$1$ and A a matrix $p$x$p$. Is it correct the following statement? $$E[(Y-\mu)(Y-\mu)'A(Y-\mu)]=AE[(Y-\mu)(Y-\mu)(Y-\mu)]=A\textbf{0}=\textbf{0} $$ Is it correct to extract matrix A in this way?