What's the matrix model of psychotherapy?

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.