Prove that if the matrix I-AB is non-singular, then so i I-BA.(adsbygoogle = window.adsbygoogle || []).push({});

This was one of my test questions and got 3 points off. Can anyone tell me what I did wrong.

my proof:

assume I-AB is nonsingular

then (I-AB)[tex]^{-1}[/tex] exists

Let C=(I-AB)[tex]^{-1}[/tex]

Consider (I+BCA)(I-BA)=I-BA+BCA-BCABA

=I-BA+BC(I-AB)A

=I-BA+B(I-AB)[tex]^{-1}[/tex] (I-AB)A

=I-BA+BIA

=I-BA+BA

=I

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# Non singular

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