$Rank = 2$ means two $non-zero$ rows. Therefore, the last row must be all $zero$. Now, let $A, B, C$ be first, second, and third row respectively. To get row $C$ all zero, the operation we need to perform is $C = 3C - B$. Therefore if $a=b=\frac{1}{3}$, the operation will cause row $C$ to be all zero. Hence option $D$ is correct.