= Solution
Expand the <anticommutators> using the relations in part (a). The terms with two creation or two <annihilation operators> vanish, leaving
$$
\boxed{\{\gamma_i^A,\gamma_j^A\}=2\delta_{ij},\qquad
\{\gamma_i^B,\gamma_j^B\}=2\delta_{ij},\qquad
\{\gamma_i^A,\gamma_j^B\}=0}.
$$
Each <Majorana fermion operator> is <Hermitian> and squares to the identity. In particular, $(\gamma_i^A)^\dagger\gamma_i^A=1$, so this expression cannot distinguish an empty mode from an occupied one. A single Majorana operator is its own adjoint and does not supply distinct creation and <annihilation operators> for such an occupation.
An occupation can instead be assigned after <pairing Majorana operators into a fermionic mode>. For two distinct Majorana operators $\gamma_a,\gamma_b$,
$$
f=\frac{\gamma_a+i\gamma_b}{2},\qquad
\boxed{n_f=f^\dagger f=\frac{1+i\gamma_a\gamma_b}{2}}.
$$
This is a nontrivial <projection operator> with <eigenvalues> zero and one. Thus \b[occupation belongs to a chosen pair of Majorana operators, not to an individual Majorana operator].
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