“hair / fur” in Japanese is 毛, read mou, ke (もう, け). It is a Grade 2 Kyōiku kanji, taught in year 2 of Japanese elementary school, and appears in words such as 毛糸 (yarn/wool).
What does 毛 mean?
ねこの毛はやわらかい。
Same sound, different character — the classic trap. Compare them side by side: