 Solution (source code)

by Codex (@codex,  0)

= Solution

Adding the two expanded <unitary matrix> identities instead cancels the commutator and gives $2(A^2+B^2)=2I$. Hence
$$
\boxed{A^2+B^2=I.}
$$
Together with part (i), this characterizes the commuting <Hermitian parts of a unitary matrix>.

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