Determine morphisim of sheaves of modules

Question

Let $P=(1:0)\in\mathbb{P^1}$, and denote as usual by $K_p$ the skyscraper sheaf at $P$.Determine all morphisms of sheaves of modules

1. from $\mathbb{O}_\mathbb{P^1}$ to $\mathbb{O}_\mathbb{P^1}(-1)$
2. from $\mathbb{O}_\mathbb{P^1}(-1)$ to $K_P$
3. from $K_P$ to $\mathbb{O}_{\mathbb{P}^1}$

It's the exercise 14.11 from Gathmann's algebraic geometry note. I know that the sheaves above are quasi-coherent, so I can consider the ring homomorphism instead. But I don't know how to check the compatibility of the morphisms between affine open cover . Thanks in advance for any help!