  Liouville field theory approach to 2-dimensional gravity possesses the
duality ($b \leftrightarrow b^{-1}$). The matrix counterpart of minimal gravity
$\mathcal{M}(q,p)$ ($q<p$ co-prime) is effectively described on $A_{q-1}$
Frobenius manifold, which may exhibit a similar duality $p\leftrightarrow q$,
and allow a description on $A_{p-1}$ Frobenius manifold. We have positive
results from the bulk one-point and the bulk-boundary two-point correlations on
disk that the dual description of the Frobenius manifold works for the unitary
series $\mathcal{M}(q, q+1)$. However, for the Lee-Yang series $\mathcal{M}(2,
2q+1)$ on disk the duality is checked only partially. The main difficulty lies
in the absence of a canonical description of trace in the continuum limit.
