Ridge and lasso with orthonormal predictors

Suppose the predictors are orthonormal, $X^TX = I$, and let $b = X^Ty$ be the OLS coefficients.

(a) Show that ridge, $\min_\beta \|y - X\beta\|^2 + \lambda\|\beta\|^2$, gives $\hat\beta_j = b_j/(1 + \lambda)$.

(b) Show that lasso, $\min_\beta \|y - X\beta\|^2 + \lambda\|\beta\|_1$, gives $\hat\beta_j = \text{sign}(b_j)\max(|b_j| - \lambda/2, 0)$.

(c) With $b = (2.4, -0.6, 1.1, -3.0)$ and $\lambda = 2$, compute both estimates.