Basic property of schemes?

Question

Let $X$ be a scheme. If $X$ happens to be affine then is it true that the canonical morphism

$$X\to\mathrm{Spec}\;\Gamma(X,\mathcal{O}_X)$$

is an isomorphism?.

Answer 1

Yes. Moreover, this property characterizes affine schemes among all locally ringed spaces. See this MO comment for a proof sketch.