gavra:
The Shulchan Aruch in O.C. 199:7 paskens that it’s a reshus. R’ Moshe Shternbuch discusses this issue in Teshuvos V’hanhagos 6:49. He asks that since we pasken that it’s a reshus (so there is nothing to lose by making a zimun) why aren’t women machmir like the shitta of the Rosh who holds that they are actually chayev to make a zimun. He suggests that zimun has a din of a beracha (using the shem umalchus from the beracha of Hazan) and it might be that the halacha that says that they are permitted to make a zimun is only if there is a tzorech, but in lieu of a tzorech it would be a beracha sheaino tzericha. He explains that the tzorech would be if there was a woman who needed someone to be motzi her and lechatchila shomea k’oneh is only permissible when you make a zimun. In Teshuvos V’hanhagos 4:51 he explains this slightly differently and adds another two reasons for women not to make a zimun, namely that it might be yuhara and that it might be lo sisgodedu if in the general populace, women don’t make a zimun. His concluding remarks there are:
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