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cmajor47
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Homework Statement
Prove: If A and B are both nxn matrices, A is invertible and AB=BA, then A-1B=BA-1
Homework Equations
(AB)-1=B-1A-1
The Attempt at a Solution
A-1B=BA-1
A-1BB-1=BA-1B-1
A-1BB-1=B(A-1B-1)
A-1(BB-1)=B(BA)-1
B-1A-1(I)=B-1B(BA)-1
(AB)-1=I(BA)-1
(AB)-1[tex]\neq[/tex]A-1B-1
Therefore A-1B does not equal BA-1
I've been struggling with proofs and was wondering if this was correct?