I get to a dead end with the 5th part

[transgalactic]

i got to a dead end with the 5th part

i tried to solve it in the llink bellow

http://img352.imageshack.us/my.php?image=img8264zj6.jpg

 

[HallsofIvy]

I had already answered this. Please stop double posting.

You are given that A²- A= -I for linear transformation A and you are asked to find A^-1. In your solution you multiply both sides by A^-1 (as I had suggested before) and get A- I= -A^-1. Then you do a lot of things that I don't understand.

Just multiply on both sides by -1 to get A^-1= I- A. What more do you want?

 

[transgalactic]

ohhh that's the answer
i thought that we need toeliminate A totally

 

[HallsofIvy]

Actually, way back where you had A(A- I)=-I you could have written that as A(I-A)= I and said "Since I-A, multiplying A give the identity, I-A must be the inverse of A!"