Prove that similar matrices have the same characteristic equations

Hello,

I have been asked on an assignment to prove that similar matrices have the same characteristic equations. I believe that I would like to prove that $\displaystyle det(A-LI) = det(M^-1AM-LI)$. (L = lambda) The only idea I have had thus far is to take the inverse of the right hand side of that equation. The farthest I have reduced that to is $\displaystyle det(MA^-1M^-1-LI)$, but even if that IS right, I don't know where to go from there. Any help would be great.

Sorry about the exponentialized -1s. I don't know how to properly display an exponent in the math code.

Thanks! (Happy)