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Suppose $X\sim N_p(\mu,\Sigma)$ . $A$ is a $p\times p$ symmetric matrix . $Q$ is defined as $Q=X^TAX$. Also $Y$ be defined as $Y=X-\mu$.

Show that $Var(Q)=2\ tr(A\Sigma A\Sigma)+4\mu^TA\Sigma A\mu$

Can someone help ? Should spectral decomposition of $A$ into eigen-values and eigenvectors be of any help?..

(I first tried to break down everything into Double-summation, so as to remove any vector of matrix, but didnt yield anything useful)

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    Entries of $X$ are mutually uncorrelated? $Q=Y'AY$? – 2017-02-04
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    @V.V $Cov(a^T Y,Y^TAY)=0$ for any fixed $a\in \Bbb{R}^p$ – 2017-02-04

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