  This note aims to give a short proof of the recent result due to
Etg\"u-Lekili (2017) and Lekili-Ueda (2021): the zigzag algebra of any finite
tree over a field of characteristic 0 is intrinsically formal if and only if
the tree is of type ADE. We also complete the proof of this result by
considering a field of arbitrary characteristic for type E, which was still
open.
