Suppose that $A$ is an $m\times n$ matrix and $B$ is an $n\times m$ matrix where $AB$ is a nonsingular matrix. Prove that

1. $\nsp{B}=\set{\zerovector}$
2. $\csp{B}\cap\nsp{A}=\set{\zerovector}$

Discuss the case when $m=n$ in connection with Theorem NPNT.