  In this paper, it is proved that the maximal violation of Mermin's
inequalities of $n$ qubits occurs only for GHZ's states and the states obtained
from them by local unitary transformations. The key point of our argument
involved here is by using the certain algebraic properties that Pauli's
matrices satisfy, which is based on the determination of local spin observables
of the associated Bell-Mermin operators.
