$X\in \mathbb{R}^n$,with mean $=\mu$, Cov $=\Sigma$. I've been trying to find $E[AXX^T]$ but I've quickly gotten stuck after reaching $AE[XX^T].$ I tried to see if I could do anything after expanding but I dont see where to go next. Any help is appreciated. (A is an $n\times n$ matrix by the way.)
$ AE[XX^T] = AE\left( \begin{array}{cccc} x_1^2 & x_1x_2 & ... & x_1x_n \\ x_2x_1 & x_2^2 & ... & x_2x_n \\ ... & ... & ... & ... \\ x_nx_1 & x_nx_2 & ... & x_n^2 \\ \end{array} \right) $