Ordinarily the barrier to rotation about a carbon-carbon double bond is quite high but compound A was observed by NMR to have a rotational barrier of only about 20 K cal / mole
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The rotational barrier for carbon-carbon double bonds is normally high (~60 kcal/mol) due to the strong π-bond. However, compound A has a significantly lower barrier (~20 kcal/mol) because the double bond is part of a conjugated system that allows for aromatic stabilization in both the three-membered and five-membered rings upon rotation. This delocalization gives the double bond substantial single bond character, drastically reducing the energy required for rotation.
Final answer: double bond having very high single bond character because of aromaticity gained in both 3 & 5 membered ring.