Am i the cause of this argument?

[PuppetLife]

So an exam is coming up and my friend, lets say her name is Lucy, needs help to study. I was casually talking to her, when I mentioned that I have work on the weekend so I probably can’t study with her, but our other friend, lets call her Helen for now, doesn’t have work and so maybe Lucy can ask Helen if she wanna study together, and ask Helen to help her. I didn’t mean anything, I was just making a suggestion. And so Lucy asked Helen if they can study together and Helen said no, and so Lucy said but she(me) said that you don’t have work this weekend. And Helen said although she doesn’t have work, she planed on studying by herself and not with other people, so she doesn’t want to study with Lucy. However Lucy can call her if she wants. Lucy then got mad at Helen, telling me that she doesn’t care anymore. And well, I’m extremely close with the two of them, and now that they are really upset/angry/mad with each other and I wonder if it is my fault. Although I’m not directly included in this argument, I feel like if I shut my mouth then maybe non of this would happen? Do I need to fix the problem? Or how can I fix it? Is it my fault?