Let $X$ be a $p\times p$ random matrix. Show that $$\mathbb{E}[Tr(X)]=Tr(E[X])$$
My solution:
$$\mathbb{E}[Tr(X)]=\mathbb{E}[\sum^p_{i=1}x_{ii}]$$
And by linearity of expectation, the RHS is equal to
$$\sum^p_{i=1}\mathbb{E}[x_{ii}]=Tr(\mathbb{E}[X])$$
Is my solution correct?