In a paper I saw the following equation.
If I express the equation in a simple way, It comes down to the following equation. $(I-A)^{-1} - (I-B)^{-1} = (I-B)^{-1} [A-B] (I-A)^{-1} $
How can we prove these are equal to each other?
Thank you
2026-04-24 03:48:47.1777002527
How to write subtraction of 2 matrix as multiplication
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Thanks for the hint @JMoravitz
With help of the hint ,the solution is
$$(I-B)^{-1} (I-B) (I-A)^{-1} - (I-B)^{-1} (I-A) (I-A)^{-1}$$ $$(I-B)^{-1} [(I-B)-(I-A)](I-A)^{-1}$$ $$(I-B)^{-1} [A-B] (I-A)^{-1}$$