Expected value of the ridge regression estimator I am trying to understand this derivation:

I think everything except the last equality is fairly simple, but I do not understand the last equality. Is there an error here?
I appreciate any help.

There's no error.
Start with $X^\top X = (X^\top X+\lambda I) - \lambda I$; premultiply both sides by $(X^\top X+\lambda I)^{-1}$. Simplify.
Postmultiply by $\beta$
