(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Q: If A and B are both nxn matrices and AB-I is invertable then prove that BA-I is also invertable.

2. Relevant equations

if A is invertible iff |A|<>0

3. The attempt at a solution

I've been thinking about this for over an hour I've only managed to prove it if either A or B are invertable. because if let's say A is invertable then:

|AB-I|<>0 => |AB-I||A|<>0 => |ABA-A|<>0 => |A||BA-I|<>0 => |BA-I|<>0 and so it's invertable. if B is invertable then you do pretty much the same thing on starting on the left side.

But what if they're both singular?

Thanks.

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# Invertible Matrices

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