factorization of a block matrix under certain conditions

Question

If $U= \begin{pmatrix} I_{s} & C_{s\times r} \\ B_{r\times s} & -I_{r} \end{pmatrix},$ then $U= \begin{pmatrix} I & -C \\ 0 & I \end{pmatrix}\begin{pmatrix} I+CB & 0 \\ 0 & I \end{pmatrix}\begin{pmatrix} I & 0 \\ B & -I \end{pmatrix}.$ How do I get this factorization? Is there a method?