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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 \(A, B\) :

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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: \(\left.A^{-1}-B^{-1}=B^{-1}(B-A) A^{-1} .\right]\)
in Mathematics by Platinum (101k points) | 216 views

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