Consider a homogeneous system of three linear equations in three unknowns represented by $\mathrm{AX}=\mathrm{O}$. If $\mathrm{X}=\left[\begin{array}{c}l \\ m \\ 0\end{array}\right], l \neq 0, m \neq 0, l, m \in \mathbb{R}$ represents an infinite number of solutions of this system, then rank of A is

• A

  3
• B

  2
• Correct answer
  C

  1
• D

  does not exist

Hence, the correct answer is option: 'C'.