How do we know the rank is 1? Here's matrix A:
$$
\begin{pmatrix}
2 & 1 \\
-4 & -2 \\
-2 & -1 \end{pmatrix}
$$
Apparently, we can determine that matrix A is of rank 1 by noting that.
$$
\det
\begin{pmatrix}
2 & 1 \\
-4 & -2 \end{pmatrix}
=
\det
\begin{pmatrix}
2 & 1 \\
-2 & -1 \end{pmatrix}
=
\det
\begin{pmatrix}
-4 & -2 \\
-2 & -1 \end{pmatrix}
=0
$$
Why does this statement guarantee that A is of rank 1? What happens, for instance, if 
$$
\det
\begin{pmatrix}
2 & 1 \\
-4 & -2 \end{pmatrix}
= 1?
$$
Also, is it possible for a matrix to be of rank 0?

The size of this matrix is $3\times 2$ so $\mathrm{rank}A\leq \min(2,3)=2$ and since the column $C_1=2C_2\not=0$ so 
$$\mathrm{rank}A=1.$$
