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I am facing problem of proving this equation below. How to prove it ?

$$({\bf A-BC})^{-1}={\bf A}^{-1}+{\bf A}^{-1} {\bf B}({\bf I+CA}^{-1} {\bf B})^{-1} {\bf CA}^{-1}$$

mathreadler
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Bingo Man
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    You can try multiply right hand side by $(\bf A-BC)$ from both left and right and simplify. If you manage to get $\bf I$ for both then you are done. – mathreadler Apr 24 '17 at 09:36

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