# Proving Linear Algebra

1. Apr 21, 2010

### annoymage

1. The problem statement, all variables and given/known data

If A and B $$\in$$ Mn(R) and B is invertible

show that

l A-cI l = l B-1AB-cI l

2. Relevant equations

N/A

3. The attempt at a solution

i've no idea how to prove this. can give me any clue?

l AI-cI l = l ABB-1-cI l

am i in the right way?

2. Apr 22, 2010

### Hoblitz

recall that for square matrices

$$det(AB) = det(A)det(B)$$

and for an invertible square matrix,

$$det(B^{-1}) = det(B)^{-1}$$

How can you apply these?