For an elementary chemical reaction, ${\mathrm{A}}_2\underset{{\mathrm{k}}_{-1}}{\stackrel{{\mathrm{k}}_1}{\rightleftharpoons }}2 \mathrm{A}$, the expression for $\frac{\mathrm{d}\left[\mathrm{A}\right]}{\mathrm{dt}}$ is

Rate $=-\frac{d\left[A\right]}{dt}=\frac{\frac{1}{2}\frac{d\left[A\right]}{dt}}{dt} \frac{d\left[A\right]}{dt}=2k_1\left[A_2\right]-2K_{-1}{\left[A\right]}^2$

$\frac{1}{2}\frac{d\left[A\right]}{dt}=k_1\left[A_2\right]-k_{-1}[A{]}^2$

Hence the correct answer is (D) $2{\mathrm{k}}_1\left[{ \mathrm{A}}_2\right]-{\mathrm{k}}_{-1}[ \mathrm{A}{]}^2$