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PostPosted: Sat Jan 21, 2017 9:52 pm 

Joined: Sat Nov 14, 2015 6:32 am
Posts: 118
Location: Melbourne, Australia
Let $A, B$ be $3 \times 3$ matrices with real entries. Prove that

$$A - \left ( A^{-1} +\left ( B^{-1} - A \right )^{-1} \right )^{-1} = ABA$$

provided all the inverses appearing on the left hand side exist.

_________________
$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^s}= \prod_{p \; \text{prime}}\frac{1}{1-p^{-s}}$


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