Let A be matrix in M_n(C) similar to unitary matrix. Is A^-1 similar to A*?

Also sprach Zarathustra Dec 2009 1,506 434 Russia May 19, 2010 #1 Let A be matrix in M_n(C) similar to unitary matrix. Is A^-1 similar to A*?

H HallsofIvy MHF Helper Apr 2005 20,249 7,909 May 20, 2010 #2 If A is similar to a unitary matrix, the it is a unitary matrix.