I am reading a book which talk about MCLT, in which they give one result that I don't understand.
Let A=$\sum _{s=1}^{n}x_sx'_s$, where $x'$ denote the transpose of $x$, $x_s=(x_{s(1)},...,x_{s(p)})$ is a p-variate random vector so that $x_s\sim \mathbb{N}_p(0,\Sigma)$ and $$\Sigma=\begin{pmatrix} \sigma_{11}&\sigma_{12}&... & \sigma_{1p}\\ \sigma_{11}&\sigma_{22}& ... & \sigma_{1p}\\ \sigma_{p1}&\sigma_{12}&... & \sigma_{pp}\\ \end{pmatrix}$$ If $x_1,..,x_n$ are i.i.d p-random vectors then, by the MCLT, we have $\frac{1}{\sqrt{n}}(A-n\Sigma)\sim \mathbb{N}_p(0,\Sigma_A)$ where $$ E(a_{ij})=n\sigma_{ij}\;\;(1)$$ and elements of $\Sigma_A$ are given by $$E(a_{ij}-E(a_{ij}))(a_{gh}-E(a_{gh}))=\sigma_{ih}\sigma_{jg}+\sigma_{ig}\sigma_{jh}\;\;(2)$$ (1) is easy, I understand that one, but (2) I don't know how they get it. I know that the covariance of A is given by $$\Sigma_A=E(A-E(A))(A-E(A))'.$$ I really need to understand this part. Your help is appriciated.