In "A Jury of Her Peers," how does the author show the reader that the women both know the identity of the murderer, and reasons?
When the two women (Mrs. Hale and Mrs. Peters) hear the men talk about how Mrs. Wright didn't keep a very nice place and that it wasn't very cheerful, Mrs. Hale said, "I don't think a place would be any the cheerfuller for John Wright's bein' in it." She had an notion from the beginning of this story that Mr. Wright was not a caring husband.
Then the women see the clues that the men miss. They see (just like the men do) how messy her kitchen was, but they know why it's messy. In this period, the kitchen was where women spent most of their time. They took care of it and it was always neat and tidy when they finished their work. They recognized that her life was not good because of how she kept her kitchen.
They see the broken hinge on the birdcage and assume that Mr. Wright killed the bird himself. They even find her "unfinished and badly sewn quilting" that she left behind. As both women put themselves in her position, living with such a horrible man, they begin seeing reasons why she would kill him. So as the men are going about their business and trying to find clues to what exactly happened, the two women hurry to fix/get rid of the only clues left behind that show what kind of life this poor Mrs. Wright was living.