2. Show that the symmetric bilinear form on H, (X,Y) → trace (XY), is nondegenerate. For & EH, define a skew-symmetric bilinear form wę on u(n) = T₁U(n) = iH (space of skew-hermitian matrices) by w (X,Y)= i trace ([X, Y]§), X,Y E iH. Check that we (X, Y) = i trace (X(Y§ – §Y)) and Y} – §Y ¤ H. Show that the kernel of wis K := {Y = u(n) | [Y, §] = 0}. ६