Chapter 4 - Vector Spaces - 4.10 Invertible Matrix Theorem II - True-False Review - Page 332: g

False

Given $nullity ([A][B]) =0$ We can notice that matrix $[A][B]$ has $2n$ columns and $n$ rows. Then $rank ([A][B]) \leq n$. From the rank nullity theorem, we have $nullity ([A][B])\geq n \gt 0$ The statement is not true.