Which hydrated elements of group $13$ are found as polymers in nature?

The correct order of atomic radii in group $13$ elements is

The structure of diborane contains:

Complete the following chemical equations:
$4BF_{3} + 3LiAlH_{4} \to 2B_{2}H_{6} (X) + 3LiF + 3AlF_{3}$
$B_{2}H_{6} (X) + 6H_{2}O \to 2H_{3}BO_{3} (Y) + 6H_{2}$
$B_{2}H_{6} (X) + 3O_{2} \xrightarrow{\Delta} B_{2}O_{3} + 3H_{2}O$

What is the product formed by the action of caustic soda on aluminum hydroxide?

$A$ compound $(A)$ of boron reacts with $NMe_3$ to give an adduct $(B)$ which on hydrolysis gives a compound $(C)$ and hydrogen gas. Compound $(C)$ is an acid. Identify the compounds $A, B$ and $C$. Give the reactions involved.