In the context of a subclass of matrix variate elliptically contoured (MEC) models, namely Laplacian MEC, with location vector and dispersion matrix , where both are unknown, Bayesian inference is considered through vague prior knowledge firstly. At the second step, an informative prior is incorporated to derive posterior distributions of and . Afterward, the main result is thoroughly considered for matrix variate Student’s t-model and thus generalizing the result of Arnold Zellner (Zellner, 1976 Zellner, A. (1976). Bayesian and non-Bayesian analysis of the regression model with multivariate Student-t error terms. J. Amer. Statist. Assoc. 71(354): 400–405.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]).