1. The problem statement, all variables and given/known data If det (AB)=0 then A or B doesn't have an inverse. True or false? 2. The attempt at a solution As det (AB)= det(A)*det(B)=0, it's clear that or det(A)=0, or det(B)=0 or both are worth 0. Meaning that there is at least A or B not inversible. But this is only true when A and B are square matrices. Because I don't think the inverse of a matrix has sense when we are talking about nxm matrices, with m different from n. Am I right? So my answer is FALSE.