Answer
This matrix is not invertible.
Work Step by Step
We use the trick in the picture:
$$ \left|\begin{matrix} 2&6&0\\1&3&2\\3&9&2 \end{matrix}\right|=2\cdot3\cdot2+6\cdot2\cdot3+0\cdot4\cdot9-3\cdot3\cdot0-9\cdot2\cdot2-2\cdot1\cdot6\\=12+36+0-0-36-12=0 $$
Since the determinant is equal to $0$, then we have, from theorem 4, that the matrix is not invertible.
