Can an author write something that is untrue in a book?

Yes, as long as it is a story book (fiction). If it isn't a work of fiction, then there shouldn't really be any mistruths in the book.

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It really depends on whether the book is fiction or non-fiction. Fiction is not true, stuff like fantasy: dragons, unicorns, etc. If an author writes something that is untrue in a non-fiction book (history, textbooks, self-help, etc.), however, it is accidental or just plain a lie. Everyone makes mistakes, even authors.