Chapter 3 - Determinants - 3.3 Properties of Determinants - 3.3 Exercises - Page 126: 58

The statement is correct.

The matrices $A$ and $B$ are square matrices of order $n$ such that $AB$ is singular. Therefore, $|AB|=0$ We can write $|AB|=|A||B|$ . Thus $|A||B|=0$ This relation implies that either $|A|=0$ or $|B|=0$ (meaning that either $A$ is a singular matrix or $B$ is a singular matrix).