- #1

daniel_i_l

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## Homework Statement

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

## Homework Equations

if A is invertible iff |A|<>0

## 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.