A first order deformation is a deformation over the dual numbers $k[t]/(t^2)$. I have read that there are no non-trivial first order deformations of complex projective space $\mathbb{P}^n$ (i.e. no first order deformations other than $\mathbb{P}^n\times \operatorname{Spec} k[t]/(t^2)\rightarrow \operatorname{Spec} k[t]/(t^2)$).
I am aware of the result for affine smooth schemes (for example here) using the infinitesimal lifting property, but am not sure how to approach this for $\mathbb{P}^n$, perhaps we use the cohomology of line bundles on $\mathbb{P}^n$?
Question: Why are there no non-trivial first order deformations on $\mathbb{P}^n$?