The complexes $\left[ Co{{\left( N{{H}_{3}} \right)}_{6}} \right]\left[ Cr{{\left( {{C}_{2}}{{O}_{4}} \right)}_{3}} \right]$ and $\left[ Cr{{\left( N{{H}_{3}} \right)}_{6}} \right]\left[ Co{{\left( {{C}_{2}}{{O}_{4}} \right)}_{3}} \right]$ shows which of the following isomerism?
A) Linkage isomerism
B) Geometrical isomerism
C) Coordination isomerism
D) Ionisation isomerism

Hint: The complexes which consist of the same molecular formula but different arrangements of atoms are known as isomers and the phenomenon is known as isomerism. In coordination compounds, the isomerism is categorized into two major parts i.e., Structural isomerism (when the change in bonding is observed) and Geometrical isomerism (when the change in the arrangement of ligands in space is observed).

Complete answer:In the given question, the complexes given are $\left[ Co{{\left( N{{H}_{3}} \right)}_{6}} \right]\left[ Cr{{\left( {{C}_{2}}{{O}_{4}} \right)}_{3}} \right]$ and $\left[ Cr{{\left( N{{H}_{3}} \right)}_{6}} \right]\left[ Co{{\left( {{C}_{2}}{{O}_{4}} \right)}_{3}} \right]$ and it is clearly observed that the bonding of ligands with the central metal ion is different which means these are categorized under structural isomerism.

Coordination isomerism: It is the type of structural isomerism in which the interchange of one or more ligands between the anionic and cationic complex is observed. In simple words, we can say that the coordination isomers are the species in which metal from one coordination sphere (cationic) gets swapped with other coordination spheres (anionic).

Example: $\left[ Co{{\left( N{{H}_{3}} \right)}_{6}} \right]\left[ Cr{{\left( CN \right)}_{6}} \right]$ is a coordination isomer of $\left[ Cr{{\left( N{{H}_{3}} \right)}_{6}} \right]\left[ Co{{\left( CN \right)}_{6}} \right]$ because the swap of metal ions is observed between the cation and anionic coordination spheres of both the complexes.
Thus, $\left[ Co{{\left( N{{H}_{3}} \right)}_{6}} \right]\left[ Cr{{\left( {{C}_{2}}{{O}_{4}} \right)}_{3}} \right]$ and $\left[ Cr{{\left( N{{H}_{3}} \right)}_{6}} \right]\left[ Co{{\left( {{C}_{2}}{{O}_{4}} \right)}_{3}} \right]$ are examples of coordination isomerism because there is an interchange of metals in the coordination sphere of both the complexes.

option (C) is correct.

Note: It is important to note that coordination isomerism can only be observed in those complexes in which both the cationic and anionic parts are complex or the bridging complexes in which the interchange of ligands or metals is possible.