I am trying to write a proof and, in order to do so, I have to simplify the following
$$ \left( E H B^{-1} \right)^b \bigg(\big(V-VH(B+HVH)^{-1}HV\big)^{bb}\bigg)^{-1}$$
where $b$ indicates the rows that should be taken from the matrix and $bb$ indicates the block that should be taken from the matrix, and $X^{-1}$ denotes the inverse of $X$. I am hence dealing with inverses of parts of a block matrix and I want to simplify this, so that i can work with matrices instead. Are there any useful books or properties that I can use?