Let $X$ denote a Gaussian column vector with mean vector $M_x=\begin{pmatrix}2 &3\end{pmatrix}$ and covariance matrix as $C_x=\begin{pmatrix}1&0\\0&1\end{pmatrix}$. The random vector $Y=AX$, where $A=\begin{pmatrix}-1&-2\\2&3\end{pmatrix}$.
Find the $\mathbb E[Y]$ and covariance matrix of $Y$.
According to my understanding, is it we have to find X first from $M_x$ and $C_x$ and then compute $Y$ and then mean of $Y$ and finally covariance matrix of $Y$. I am not sure about the formulas as well but I was thinking if this is how we need to do this? Thanks for any suggestions.
In general if $\mu_{X}$ is a notation for the mean of $X$ and $\Sigma_{X}$ is a notation for the covariance matrix of $X$ then: $$\mu_{AX}=A\mu_{X}\text{ and }\Sigma_{AX}=A\Sigma_{X}A^{T}$$where $A$ denotes a matrix such that $AX$ is well defined.