$\mathrm{A}, \mathrm{C}$ are $3 \times 3$ matrices. $\mathrm{B}, \mathrm{D}$ are $3 \times 1$ matrices. If $\mathrm{AX}=\mathrm{B}$ has unique solution and $\mathrm{CX}=\mathrm{D}$ has infinite number of solutions, then

• A

  $\operatorname{rank}$ of $[\mathrm{A}: \mathrm{D}]=\operatorname{rank}$ of $[\mathrm{C}: \mathrm{B}]$
• B

  $\operatorname{rank}$ of $\mathrm{A}=\operatorname{rank}$ of C
• C

  $\operatorname{rank}$ of $[\mathrm{A}: \mathrm{B}] < \operatorname{rank}$ of $[\mathrm{B}: \mathrm{D}]$
• Correct answer
  D

  $\operatorname{rank}$ of $[\mathrm{A}: \mathrm{D}] \geq \operatorname{rank}$ of $[\mathrm{C}: \mathrm{B}]$

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