- #1
eyehategod
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Prove that if the matrix I-AB is non-singular, then so i I-BA.
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
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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