= Solution
Write the <adjunction unit> as $\eta:1_{\mathcal C}\Rightarrow GF$ and the <adjunction counit> as $\varepsilon:FG\Rightarrow1_{\mathcal D}$. Define the <monad induced by an adjunction> by
$$
\boxed{T=GF,\qquad \mu_A=G\varepsilon_{FA}:GFGFA\to GFA,}
$$
with unit $\eta$. <Naturality> of $\varepsilon$ makes $\mu$ a <natural transformation>.
The <triangle identities for an adjunction> give the two unit laws:
$$
\mu_A\eta_{TA}=G\varepsilon_{FA}\eta_{GFA}=1_{GFA},\qquad
\mu_A T\eta_A=G(\varepsilon_{FA}F\eta_A)=1_{GFA}.
$$
For associativity, apply <naturality> of $\varepsilon$ to the arrow $\varepsilon_{FA}:FGFA\to FA$ in $\mathcal D$:
$$
\varepsilon_{FA}FG\varepsilon_{FA}=\varepsilon_{FA}\varepsilon_{FGFA}.
$$
Applying $G$ yields
$$
\mu_A T\mu_A=\mu_A\mu_{TA}.
$$
Thus the induced data satisfy all the <monad> laws, rather than merely supplying an <endofunctor> and two transformations.
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