  In this article, we study the Berglund--H\"ubsch transpose construction W^T
for invertible quasihomogeneous potential W. We introduce the dual group G^T
and establish the state space isomorphism between the Fan-Jarvis-Ruan-Witten
A-model of W/G and the orbifold Milnor ring B-model of W^T/G^T. Furthermore, we
prove a mirror symmetry theorem at the level of Frobenius algebra structure for
G^max. Then, we interpret Arnol'd strange duality of exceptional singularities
W as mirror symmetry between W/J and its strange dual W^SD.
