To evaluate the assertion and the reason, let's first analyze the given complex ion $$[\mathrm{Co}(\mathrm{en})_2 \mathrm{Cl}_2]^{+}$$.

1. Assertion (A): The total number of geometrical isomers shown by $$[\mathrm{Co}(\mathrm{en})_2 \mathrm{Cl}_2]^{+}$$ complex ion is three.

2. Reason (R): $$[\mathrm{Co}(\mathrm{en})_2 \mathrm{Cl}_2]^{+}$$ complex ion has an octahedral geometry.

First, we know that $$[\mathrm{Co}(\mathrm{en})_2 \mathrm{Cl}_2]^{+}$$ is a coordination complex with $$\mathrm{Co}$$ (Cobalt) in the center coordinated to two ethylenediamine (en) ligands and two chlorides (Cl). Ethylenediamine is a bidentate ligand, meaning it binds through two donor atoms, giving the overall complex an octahedral geometry around the central cobalt ion.

To verify the assertion about the geometrical isomers:

In an octahedral complex, the two chlorides and the two $$\mathrm{en}$$ ligands can have different spatial arrangements relative to each other. Specifically, for $$[\mathrm{Co}(\mathrm{en})_2 \mathrm{Cl}_2]^{+}$$, the possible geometrical isomers are:

• cis-isomer: where the two chlorides are adjacent to each other.
• trans-isomer: where the two chlorides are opposite each other.

These two configurations are the typical geometrical isomers for this type of complex. Thus, the assertion that there are three geometrical isomers appears incorrect, as the common understanding is that there are only two geometrical isomers for this type of octahedral complex.

Now, let’s consider the reason:

The reason states that $$[\mathrm{Co}(\mathrm{en})_2 \mathrm{Cl}_2]^{+}$$ has an octahedral geometry. This statement is indeed correct because the coordination number of 6 (from the four donor atoms of the two $$\mathrm{en}$$ ligands and the two chloride ions) leads to an octahedral geometry.

Therefore, the most appropriate answer is:

Option B: (A) is not correct but (R) is correct