this is not an answet but just a comment but the comment thing does not work. Ok i understamd .I forgot to come back here and correct my mistake same day i posted it should have been written:

(ma:ident(3),ma[1,1]:%i/2,ma[1,3]:sqrt(3)/2,ma[3,1]:sqrt(3)/2,ma[3,3]:%i/2,ma)

Then do conjugate(transpose(ma)).ma; and get unit matrix

Unfortunately is not hermetian which is what is wanted also want not in the form of cst times a unit matrix. So i did

(ma:ident(3),ma[1,1]:%i/2,ma[1,3]:sqrt(3)/2,ma[3,1]:sqrt(3)/2,ma[3,3]:%i/2,ma[1,1]:-1/2,ma[3,3]:1/2,disp(["ma init"=ma,"ma aft"=ma,"ma.ma"=ma.ma]));(ma[1,1]:-1/2,ma[3,1]:1/2,ma[1,3]:%i*ma[3,1],ma.ma )

Yea i know i have noticed that before but still guess that is one of the most stubborn and inconvenient characteristics of matrices - as far as i can tell the diagonal entries of a hermetian must be real or it's not Hermetian ? Thankyou