Question 40403
A AND B ARE COMPLEX HERMITIAN MATRICES OF ORDER (N,N)						
LET TRANSPOSE OF A AND B BE A' AND B'						
SINCE A,B ARE HERMITIAN,WE HAVE 						
A=CONJUGATE (A') AND B= CONJ(B')……………………….I						
CASE 1.						
AB IS HERMITIAN.LET AB=C…..SO AB=C=CONJ(C')=CONJ(AB)'…………..II						
C'=(AB)'=B'A'						
CONJ(C')=CONJ(B'A')=CONJ(B')CONJ(A')=BA…FROM I						
BUT AB=CONJ(C') FROM II						
SO AB=BA						
CASE 2.						
AB=BA= CONJ(B')CONJ(A')=CONJ(B'A')=CONJ(AB)'=AB…..						
HENCE AB IS HERMITIAN.