Statement A:  Due to the presence of zygospore, a group of fungi is called zygomycetes.
Statement B: Zygospore is the site of meiosis and give rise to new mycelium directly. 

Sexual reproduction produces a resting diploid spore called zygospore. Because of the presence of zygospore, the group of fungi is called zygomycetes.
Zygospore is the site of meiosis and does not give rise to new mycelium directly. Instead it produces a new sporangium called germ sporangium.