Solution
= Solution
If the multiplication in the <unit and multiplication of a monad> $\mu$ is invertible, the two unit identities of the <monad>
$$
\mu\circ T\eta=1_T,\qquad \mu\circ\eta T=1_T
$$
make both $T\eta$ and $\eta T$ its inverse. Hence \b[idempotence implies equality of the two unit insertions]:
$$
\boxed{T\eta=\eta T=\mu^{-1}.}
$$
This is the first implication in the characterization of an <idempotent monad>.