Solution
= Solution
\b[True.] The hypothesis says that $\alpha+\alpha$ and $\beta$ commute under <ordinal addition>. By the <commuting ordinal addition> classification, comparison of their <Cantor normal forms> implies that $\alpha$ and $\beta$ themselves commute. Therefore
$$
\alpha+\alpha+\beta
=\alpha+\beta+\alpha
=\beta+\alpha+\alpha,
$$
so both outer expressions equal the middle one.