## Regression proof

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

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