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For non-zero real numbers one uses $\frac{1}{a}-\frac{1}{b}=\frac{b-a}{a b}$. Verify the following analog for invertible matrices $A, B$ :
$A^{-1}-B^{-1}=A^{-1}(B-A) B^{-1}$
[The following version is also correct: $\left.A^{-1}-B^{-1}=B^{-1}(B-A) A^{-1} .\right]$
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