# 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 $$\beta$$