  We consider entanglement of first-quantized identical particles by adopting
an algebraic approach. In particular, we investigate fermions whose wave
functions are given by the Slater determinants, as for singlet sectors of
one-matrix models. We show that the upper bounds of the general R\'enyi
entropies are $N \log 2$ for $N$ particles or an $N\times N$ matrix. We compute
the target space entanglement entropy and the mutual information in a free
one-matrix model. We confirm the area law: the single-interval entropy for the
ground state scales as $\frac{1}{3}\log N$ in the large $N$ model. We obtain an
analytical $\mathcal{O}(N^0)$ expression of the mutual information for two
intervals in the large $N$ expansion.
