We consider 9 Gaussian matrix ensembles characterized by single symmetry among the 38-fold symmetry classification classes of non-Hermitian random matrices, and establish exact duality formulae of certain observables between them. Particularly, averaged products of K characteristic polynomials in an <math><mi>N</mi><mo>×</mo><mi>N</mi></math> matrix ensemble can be expressed in terms of another <math><mi>K</mi><mo>×</mo><mi>K</mi></math> matrix ensemble. Our method is to combine matrix-valued heat equations and differential identities for determinants and Pfaffians and has more possible applications.