An inorganic compound $$'A'$$ shows the following reactions :
(i) It is white solid, exists as dimer and fumes in wet air.
(ii) It sublimes at $$180{\,^ \circ }C$$  and forms monomer if heated to $$400{\,^ \circ }C.$$
(iii) Its aqueous solution turns blue litmus to red and gives a white precipitate with $$AgN{O_3}$$  solution, which is soluble in $$N{H_4}OH.$$
(iv) Addition of $$N{H_4}OH$$  and $$NaOH$$  separately to the solution of $$'A'$$ gives a gelatinous precipitate which in however soluble in excess of $$NaOH.$$
The compound $$'A'$$ is

Solution :
Compound $$'A'$$ is $$A{l_2}C{l_6}.$$
(i) $$A{l_2}C{l_6}$$  is a white solid, exists as dimer and fumes in wet air.
(ii) It sublimes at $$180{\,^ \circ }C$$  and converts into $$AlC{l_3}$$  at $$400{\,^ \circ }C.$$
(iii) Its aqueous solution is acidic, so it turns blue litmus to red.
$$A{l_2}C{l_6} + 6{H_2}O \to $$     $$\mathop {2Al{{\left( {OH} \right)}_3}}\limits_{{\text{weak base}}} + \mathop {6HCl}\limits_{{\text{strong acid}}} $$
It gives white $$ppt.$$  with $$AgN{O_3}$$  which is soluble in $$N{H_4}OH.$$
$$\left( {{\text{iv}}} \right)AlC{l_3} + 3NaOH \to $$     $$\mathop {Al{{\left( {OH} \right)}_3}}\limits_{{\text{white ppt}}{\text{.}}} + 3NaCl$$
$$Al{\left( {OH} \right)_3} + \mathop {NaOH}\limits_{{\text{excess}}} \to $$     $$\mathop {NaAl{O_2}}\limits_{{\text{soluble}}} + 2{H_2}O$$
But in case of $$N{H_4}OH,$$  the $$ppt.$$  of $$Al{\left( {OH} \right)_3}$$  does not dissolve in excess of $$N{H_4}OH.$$