- #1

Random Variable

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- 0

## Homework Statement

Show that A and Inverse(I+A) commute (where I is the identity matrix).

## Homework Equations

Inverse(Inverse(A))=A

Inverse(AB)=Inverse(B)*Inverse(A)

## The Attempt at a Solution

My solution assumes the existence of the inverse of A.

A*Inverse(I+A) = Inverse(Inverse(A))*Inverse(I+A)

= Inverse[(I+A)*Inverse(A)]

= Inverse[Inverse(A)+I]

= Inverse[Inverse(A)*(I+A)]

= Inverse(I+A)*Inverse(Inverse(A))

= Inverse(I+A)*A

My professor told me that the inverse of A may or may not exist. Does he want me to prove that it does exist? Can you even prove it does exist from the fact that the inverse of (I+A) exists? Does he want a different proof? Is he just giving me a hard time?