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An equality with matrices

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Riemann
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An equality with matrices

#1

Post by Riemann » Sat Jan 21, 2017 9:52 pm

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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