Let V be the space of all n×1 matrices over C, A an n×n matrix over C, and f the bilinear form on V given by f(X,Y)=XtAY. Show that f is invariant under O(n,C), i.e., f(MX,MY)=f(X,Y) for all X, Y in V and M in O(n,C), if and only if A commutes with each member of O(n,C).