Let $A,B\in \mathbb{R}^{n\times d}$, where $d\ge n$ and every entry of $A$ and $B$ is iid standard normal. I am studying expectation involving $A^\top (B B^\top)^{-1}A$ and $A^\top (B B^\top)^{-2}A$. I was wondering if their distributions have a name so that I could find related works.
Thank you!