Could you help me solve the following exercise (which I saw in the book: An Algebraic Introduction to Complex Projective Geometry by Peskine, page 210).
Let $R$ be a Noetherian normal domain. Let $I$ be a reflexive ideal. Assume that $I = (a, b)$. Show that the kernel of the surjective map $R^2 \overset{(a, b)}{\to } I$ is isomorphic to $I^* = \mathrm{Hom}(I, R)$.