Proving Linear Algebra Statement: A and B in Mn(R) with B invertible

[annoymage]

Homework Statement

If A and B \in M_n(R) and B is invertible

show that

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

Homework Equations

N/A

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?

 

[Hoblitz]

recall that for square matrices

<br /> <br /> det(AB) = det(A)det(B)<br /> <br />

and for an invertible square matrix,

<br /> <br /> det(B^{-1}) = det(B)^{-1}<br /> <br />

How can you apply these?