$PV = RT$ for 1 mole of gas
At constant T : $(\large\frac{\delta V}{\delta P})_T = -\large\frac{V}{P}$
At constant V : $(\large\frac{\delta P}{\delta T})_V = \large\frac{R}{V}$
At constant P : $(\large\frac{\delta V}{\delta T})_P = \large\frac{R}{P}$
$\therefore (\large\frac{\delta P}{\delta T})_V.(\large\frac{\delta V}{\delta T})_P . (\large\frac{\delta V}{\delta T})_T = \large\frac{-R^2V}{P^2V} = -\large\frac{R^2}{P^2}$
Hence answer is (A)