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## Homework Statement

For the invertible matrices A, B and A-B, simplify the expression [tex](A - B)^{-1}A(A^{-1} - B^{-1})B[/tex].

## Homework Equations

properties of invertible matrices

## The Attempt at a Solution

[tex](A - B)^{-1}A(A^{-1} - B^{-1})B[/tex]

= [tex](A - B)^{-1}(AA^{-1}B - AB^{-1}B)[/tex]

= [tex](A - B)^{-1}(IB - AI)[/tex]

= [tex](A - B)^{-1}(B - A)[/tex]

= [tex]I[/tex]

Am I correct?