Step 1: Concept
For cis-trans (geometrical) isomerism, each carbon of the double bond must be attached to two different groups.
Step 2: Analysis of But-1-ene
The structure is $\text{CH}_2 = \text{CH}-\text{CH}_2-\text{CH}_3$.
- The first carbon ($\text{C}_1$) is attached to two identical Hydrogen atoms ($-\text{H}$ and $-\text{H}$).
Step 3: Conclusion
Because one of the doubly bonded carbons has two identical groups, rotation or swapping does not create a new spatial arrangement. Therefore, it cannot show cis-trans isomerism.
Final Answer: (A)