This is not a homework question, but a small part in understanding a research paper.
Let $A$ and $B$ be two matrices, where $A_{ij} \sim \mathcal{N}(\mu_1, \Sigma_1)$ and $B_{ij} \sim \mathcal{N}(\mu_2, \Sigma_2)$, respectively. What can we say about the distribution of the entries of the matrix $AB$, where $A$ and $B$ have size that permits matrix multiplication?
