# Invertible matrix help

1. Oct 21, 2008

### FancyChancey

Hi all. I'm having a real tough time with this question. I don't know where to begin and how to go about the question. Can someone point me in the right direction please?

(Problem is on the attachment)
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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2. Oct 21, 2008

### HallsofIvy

Staff Emeritus
Re: Matrices

haven't we seen this before?

a) If A is invertible, then (A+ 2A-1) is invertible.
When does there exist a matrix, B, such that (A+ 2A-1)B= I?
If I remember correctly, a matrix is invertible if and only if it's determinant is not 0. What is the determinant of A+ 2A-1?

b) If a real matrix B satisfies B2- 2B+ 1= 0, then B-I cannot be invertible.
B2- 2B+I= (B- I)2

c) There is a non-invertible matrix, B, satisfying B2- 2B+ I= 0.
As I said, B2-2B+ I= (B-I)2. Therefore B= ? or ?. Is either of those non-invertible?