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

Show that $\displaystyle B_\lambda=(I+\lambda (X^T X)^ {-1}B_*$ where $\displaystyle 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