  In our previous papers, the Wronskian identities for the Hermite, Laguerre
and Jacobi polynomials and the Casoratian identities for the Askey-Wilson
polynomial and its reduced form polynomials were presented. These identities
are naturally derived through quantum mechanical formulation of the classical
orthogonal polynomials; ordinary quantum mechanics for the former and discrete
quantum mechanics with pure imaginary shifts for the latter. In this paper we
present the corresponding identities for the discrete quantum mechanics with
real shifts. Infinitely many Casoratian identities for the $q$-Racah polynomial
and its reduced form polynomials are obtained.
