  We discuss twisted bilayer graphene (TBG) based on a theorem of flat band
ferromagnetism put forward by Mielke and Tasaki. According to this theorem,
ferromagnetism occurs if the single particle density matrix of the flat band
states is irreducible and we argue that this result can be applied to the
quasi-flat bands of TBG that emerge around the charge-neutrality point for
twist angles around the magic angle $\theta\sim1.05^\circ$. We show that the
density matrix is irreducible in this case, thus predicting a ferromagnetic
ground state for neutral TBG ($n=0$). We then show that the theorem can also be
applied only to the flat conduction or valence bands, if the substrate induces
a single-particle gap at charge neutrality. Also in this case, the
corresponding density matrix turns out to be irreducible, leading to
ferromagnetism at half filling ($n=\pm2$).
