Complex Analysis analytic function 1$f(z)=z$

Question

if$\text{ } f:D(0,1)\longrightarrow D(0,1)$

is analytic such that there exists

$a,b\in D(0,1)$ and $\text{ }$$f(a)=a$ , $f(b)=b$

prove that $f(z)=z$ $\forall$ $z\in D(0,1)$

Answer 1

Hint: Use the Schwarz lemma. ${}$