Question

how did the narrator conclude that she was right

Answer 1

The narrator concluded that she was right as when she saw the table cloth with a burnt mark on it.

Answer 2

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The woman was wearing the green knitted cardigan of the narrator’s mother. The wooden buttons were rather pale from washing. She saw that the narrator was looking at the cardigan. She half hid herself again behind the door. Her reaction convinced the narrator that she was right.