Show that the contrasts in the TijS corresponding to the contrasts E Aiai and E E Ai''lj (a{3)ij are E E AiTij and E E Ai''ljTij, respectively.

Hint: Any contrast in the TijS corresponds to a vector in C(Mr), just as any contrast in the aiS corresponds to a vector in C(Ma) C C(Mr). Recall that contrasts are only defined up to constant multiples; and that contrasts in the aiS also involve the interactions when interaction exists.