A free living nitrogen-fixing cyanobacterium which can also form symbiotic association with the water fern Azolla is:

Step-by-step solution

Azolla (water fern) and the blue-green alga Anabaena azollae maintain a symbiotic relationship where the alga provides nitrogen to the fern, and the fern provides a habitat for the alga. Related Theory Frankia show nitrogen fixation in both symbiotic association with actinorhizal plants, Casuarina and free-living aerobic conditions, while most Rhizobia fixes nitrogen in symbiotic form only.