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formula on real-time rendering

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I have a question about a formula in the book real-time rendering 2nd. In 3rd chapter, at the end of 'The Rigid-Body Transform' part you can see formula that uses conjugate of rotation matrix to get inversion matrix of X. But I don't understand why conjugate is used in here. Could somebody explain this to me, please? And this is the link of the book on google(It on page 34). http://books.google.co.kr/books?id=mOKEfBTw4x0C&printsec=frontcover&dq=real+time+rendering&lr=&cd=1#v=onepage&q=&f=false

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On way to get the inverse of a matrix is to get the conjugate/adjooint matrix (which is the transposed cofactror matrix) and divide each element by the determinant.

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