  We prove the integrability of the two-loop open spin chain Hamiltonian from
ABJM determinant like operators given in arXiv:1809.09941. By explicitly
constructing R-matrices and K-matrices, we successfully obtain the two-loop
Hamiltonian from the double row transfer matrices. This proves the
integrability of our two-loop Hamiltonian. Based on the vacuum eigenvalues of
the transfer matrices, we make a conjecture on the eigenvalues of the transfer
matrices for general excited states. Bethe ansatz equations are simply obtained
from the analytic conditions at the superficial poles of the eigenvalues.
