For reaction a $\mathrm{A}\to \mathrm{x}\mathrm{P},$ when [A] = 2.2 mM, the rate was found to be 2.4 $\mathrm{mM}{\mathrm{s}}^{-1}$. On reducing concentration of A to half, the rate changes to 0.6 $\mathrm{mM}{\mathrm{s}}^{-1}$. The order of reaction with respect to A is 

$aA\to xP$

Rate of reaction $={\left[\mathrm{A}\right]}^{\mathrm{a}}$

Order of reaction = a

${\left[\mathrm{A}\right]}_1=2.2 \mathrm{mM}, {\mathrm{r}}_1=2.4 \mathrm{mM} {\mathrm{s}}^{-1} ...... (\mathrm{i})$

${\left[\mathrm{A}\right]}_2=2.2/2{\text{ mM, r}}_2=0.6{\text{ mM s}}^{-1}\text{ or, }\frac{2.4}{4}.....\left(\mathrm{ii}\right)$

On reducing the concentration of A to half, the rate of reaction is decreased by four times. 

Rate of reaction $={\left[\mathrm{A}\right]}^2$

Order of reaction = 2.