Select the correct statement about the complex \([ \text{Co}(\text{NH}_3)_5 \text{SO}_4 ] \text{Br}\).
Let's analyze each of the statements:
1. Ionisation isomer: Ionisation isomers are formed when the counter-ion (such as Br\(^-\) or SO\(_4^{2-}\)) exchanges places with the ligand. For the given complex \([ {Co}({NH}_3)_5 {SO}_4 ] {Br}\), the ionisation isomer can be formed by switching the counter-ion and the ligand, resulting in \([ {Co}({NH}_3)_5 {Br}] {SO}_4 \). Thus, statement (A) is correct.
2. Precipitation with AgNO\(_3\): When the complex is treated with AgNO\(_3\), the bromide ion (Br\(^-\)) will react with Ag\(^+\) to form a yellow precipitate of AgBr. Thus, statement (B) is correct.
3. Precipitation with BaCl\(_2\): The ionisation isomer of the complex \([ {Co}({NH}_3)_5 {Br}] {SO}_4 \) contains the sulfate ion (SO\(_4^{2-}\)), which reacts with BaCl\(_2\) to form a white precipitate of BaSO\(_4\).
Therefore, statement (C) is also correct. Since all the statements are correct, the correct answer is \( \boxed{{D}} \), All the above are correct statements.