A question in finding a invert of a certain operator

1. Mar 8, 2008

2. Mar 8, 2008

HallsofIvy

Staff Emeritus
You are given that A2- A+ I= 0. Just basic algebra tells you that is the same as I= A- A2= A(I- A). Now, stop worrying about formulas, etc. and think about what A-1 means.

3. Mar 8, 2008

transgalactic

it means that if we take the image of a certain basis
and put it into the A^-1 we get the original basis

how its gonna help me??

thought of certain solution of making some basic multiplication
operations

i got the resolt

A^-1=I-A
is it ok??

Last edited: Mar 8, 2008
4. Mar 8, 2008

HallsofIvy

Staff Emeritus
?? No, A-1 doesn't mean anything like that: it means the linear operation that "undoes" A. A-1Ax= x and AA-1x= x.

My point was that A(I- A)= I shows that I -A does exactly what we want of the inverse: AA-1= I. Since A(I-A)= I, (and inverses are unique), A-1= I- A.

5. Mar 8, 2008