Answer: $C$
Determinant comes out to be $0$. So, rank cannot be $3$. The minor $\begin{bmatrix} 3 & 5 \\[0.3em] 1 & 1 \\[0.3em] \end{bmatrix}\neq0.$ So, rank is $2.$
(OR)
If we do elementary row operations on the given matrix then we get
$\begin{bmatrix}0&0&-3\\9&3&5\\3&1&1\end{bmatrix} \overset{R_2\leftarrow R_2 - 3R_3}{\to} \begin{bmatrix}0&0&-3\\0&0&2\\3&1&1\end{bmatrix}$
$\overset{R_1 \leftarrow R_1 + \frac{3}{2}R_2}{\to} \begin{bmatrix}0&0&0\\0&0&2\\3&1&1\end{bmatrix}\overset{R_1 \leftrightarrow R_3}{\to} \begin{bmatrix}3&1&1\\0&0&2\\0&0&0\end{bmatrix}$
As the number of non zero rows is $2$, the rank of the matrix is also $2.$