I am stuck on one step that occurs without explanation in several Algebraic geometry books. 

Starting from the exact sequence

$$0\rightarrow \Omega_{\mathbb{P}^n}\rightarrow \mathcal{O}_{\mathbb{P}^n}(-1)^{\oplus n+1}\rightarrow \mathcal{O}_{\mathbb{P}^n}\rightarrow 0$$

it is concluded that $$\omega_{\mathbb{P}^n}=\wedge^n \Omega_{\mathbb{P}^n}\cong \mathcal{O}_{\mathbb{P}^n}(-n-1)$$

How does this follow and in particular how does $\Omega_{\mathbb{P}^1}\cong \mathcal{O}_{\mathbb{P}^1}(-2)$ follow ?

Thanks in advance.