Any suggestions at to what matrix $B$ is such that$\|X[(I+YX)^{-1}-I]-BY\|=O(\|Y^a\|)$ where $a>1$ and $X,Y,B$ are all square matrices of the same size and $I$ is the identity matrix and $\|\cdot\|$ is a norm?
Also, to be clear $O(\cdot)$ is the big-$O$ notation .
Thank you.