Centrosymmetric and reverse matrices in bivariate orthogonal polynomials

We study bivariate orthogonal polynomials associated with an inner product that satisfies a symmetry property such that it is invariant when both variables are interchanged. Under that hypothesis, the structure of the polynomial vectors of the orthogonal polynomial systems is described by using centrosymmetric matrices. Also, we prove that the coefficient matrices of the three term relations, one for each variable, are connected by a reverse operation over matrices. Finally, several particular cases and examples are analysed.