Exercise 1.3.10

If $N(A)$ is zero vector, the for $B=\left[\begin{array}{ccc}\hfill A\hfill & \hfill A\hfill & \hfill A\hfill \end{array}\right]$, its nullspace is also zero vector, since for $\mathit{Bx}=0$, we need to make $\left[\begin{array}{ccc}\hfill \mathit{Ax}\hfill & \hfill \mathit{Ax}\hfill & \hfill \mathit{Ax}\hfill \end{array}\right]=0$, which dictates each $\mathit{Ax}=0$, which has only zero solution. So the $N(B)$ is also zero vector.