Let  Y=XB+\varepsilon ,   \varepsilon ~ N(0,\sigma^2, I)
Let  B_\lambda be the ridge estimator define to minimize ||Y-XB||^2<br />
+ \lambda||B||^2 , \lambda > 0.

Show that B_\lambda=(I+\lambda (X^T X)^ {-1}B_* where  B_* is the least square estimator for B

I dont really have any idea of how to begin

Any help will be appreciated

Thanks in advance