True or false, about determinant (linear algebra)

[fluidistic]

Homework Statement

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.

 

[mighty2000]

Your analysis is correct. The statement is only true for square matrices, as the concept of inverse does not apply to non-square matrices. Therefore, the statement should be qualified to specify that A and B are square matrices in order for it to be true. Otherwise, it is false.