Suppose $\Omega\subset\mathbb{C}^n$ is a bounded strongly pseudoconvex domain with $C^2$ boundary. Prove that
(a) There is a $C^2$ defining function $r$ of $\Omega$ (i.e.,$\Omega=\{r<0\}$ and $dr|_{\partial \Omega}\neq 0$) such that$(\frac{\partial^2 r}{\partial z_i\partial \bar{z_j}})$ is (Hermitian) positive-definite on $\partial\Omega$.
(b) For all $p\in\partial\Omega$, there is a biholimorphic map $f$ defined in the neighborhood $U$ of $p$ such that $f(U\cap\Omega)$ is strongly convex at $f(p)$.
For (a), I understand the definition of psedoconvexity is independent of the choice of defining function. However, I have not got the suitable defining function through the calculation.
Appreciate any help!