This is a homework problem I’m trying to solve but I can’t seem to solve Q1b without using the theorem.

I am also given the fact that

$$E(y’Ay)=tr(A\Sigma)+\mu’A\mu$$

I’ve tried using the trace-expectation trick but to no avail. Assuming $y\sim N(0,I)$, $$\begin{align*} var(y’Ay) &=E[(y’Ay-tr(A))^2]\\ &=E(y’Ayy’Ay)-tr(A)^2\\ &=E(tr[y’Ayy’Ay])-tr(A)^2\\ &=E(tr[Ayy’Ayy’])-tr(A)^2\\ &=tr(E[Ayy’Ayy’])-tr(A)^2\\ &=tr(AE[yy’Ayy’])-tr(A)^2 \end{align*} $$ Then I’m stuck.