Which of the following statements regarding `1,3`- dimethyl cyclobutane is/are correct?

Options

A. Both cis and trans forms are optically active.
B. Both cis and trans forms are optically inactive.
C. The cis form is optically active, while the trans form is optically inactive.
D. The trans form is optically active, while the cis form is optically inactive.

Answer

To determine which statements regarding 1,3-dimethylcyclobutane are correct, we will analyze the structure and optical activity of both the cis and trans forms of the compound.

### Step-by-Step Solution:

1. **Understanding the Structure**:
- 1,3-dimethylcyclobutane consists of a cyclobutane ring with two methyl groups attached at the 1 and 3 positions.
- The two possible configurations for these methyl groups are cis (both groups on the same side of the ring) and trans (the groups on opposite sides of the ring).

2. **Drawing the Structures**:
- **Cis form**: Both methyl groups are on the same side (wedge-wedge or dash-dash).
- **Trans form**: One methyl group is on a wedge (up) and the other on a dash (down).

3. **Analyzing Optical Activity**:
- A compound is optically active if it does not possess any symmetry elements that would allow it to be superimposed on its mirror image.
- For a compound to be optically inactive, it must have either a center of symmetry, a plane of symmetry, or an axis of symmetry.

4. **Checking for Symmetry**:
- **Cis form**: When you draw a plane of symmetry through the center of the cyclobutane, it divides the molecule into two equal halves. Therefore, the cis form has a plane of symmetry and is optically inactive.
- **Trans form**: Similarly, if you draw a plane of symmetry for the trans form, it also divides the molecule into two equal halves. Thus, the trans form also has a plane of symmetry and is optically inactive.

5. **Conclusion**:
- Since both the cis and trans forms of 1,3-dimethylcyclobutane have a plane of symmetry, both are optically inactive.

### Final Answer:
The correct statement regarding 1,3-dimethylcyclobutane is that **both cis and trans forms are optically inactive**.