= Solution
A <unital quantum channel> preserves the identity operator: $\Phi(I)=I$. In equal input and output dimensions, it therefore preserves the <maximally mixed state>. For <amplitude damping channel>,
$$
\mathcal A_p(I)=K_0K_0^\dagger+K_1K_1^\dagger=\begin{pmatrix}1+p&0\\0&1-p\end{pmatrix}=I+pZ.
$$
Hence \b[the channel is not unital for $p>0$; it is unital only in the identity case $p=0$]. Trace preservation involves the opposite products $K_i^\dagger K_i$ and does not imply unitality.
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