Addiction treatment. Primarily aimed at addition, the matrix model is an outpatient model of treatment focusing on behavior (rather than underlying 'issues') and accountability to therapist, with whom a positive therapeutic alliance is crucial (perhaps the lynchpin of the entire model). Other aspects of the model are a potpourri of common interventions, e.g. Psychoeducation, 12-step, family involvement, etc.
Not enough info. I am an expert in psychotherapy and am unfamiliar with the term. It may refer to an approach developed by a particular clinic or group, not a mainstream model of psychotherapy. Mainstream therapy approaches include, for example, psychodynamic therapy, cbt, ipt (interpersonal psychotherapy), and so on. You should probably be asking the person recommending this treatment a lot more questions.