  In this paper, by introducing new matrix operations and using a specific
inverse relation, we establish the dual forms of the orthogonality relations
for some well-known discrete and continuous q-orthogonal polynomials from the
Askey-scheme such as the little and big q-Jacobi, q-Racah, (generalized)
q-Laguerre, as well as the Askey-Wilson polynomials. As one of the most
interesting results, we show that the Askey-Wilson q-beta integral represented
in terms of the VWP-balanced 8{\phi}7 series is just a dual form of the
orthogonality relation of the Askey-Wilson polynomials.
