Identify the correct statements from the following : I. $\mathrm{Ga}_2 \mathrm{O}_3$ is an amphoteric oxide. II. The dimer of aluminium chloride has three $\mathrm{Al}-\mathrm{Cl}-\mathrm{Al}$ bridge bonds. III. Boron is very hard refractory solid of high melting temperature.

(I) $\mathrm{Ga}_2 \mathrm{O}_3$ is an amphoteric oxide is the correct statement as it reacts with acid and base both, as shown below : Reaction with an acid $$ \mathrm{Ga}_2 \mathrm{O}_3+6 \mathrm{HCl} \longrightarrow 2 \mathrm{GaCl}_3+3 \mathrm{H}_2 \mathrm{O} $$ Reaction with a base $$ \mathrm{Ga}_2 \mathrm{O}_3+2 \mathrm{NaOH} \longrightarrow 2 \mathrm{NaGaO}_2+\mathrm{H}_2 \mathrm{O} $$ (II) The dimer of aluminium chloride has three $\mathrm{Al}-\mathrm{Cl}-\mathrm{Al}$ bridge bond is not the correct statement as structure of $\mathrm{Al}_2 \mathrm{Cl}_6$ is as follows:
(III) Boron is very hard refractory solid of high melting temperature is the correct statement as its melting point is $2349 \mathrm{~K}$ and is used as refractory solid. Hence, option (b) is the correct answer.