Complete 20.12, 21.2b, 21.3 (use R).  For 20.12, note that the second-order terms in second-order polynomials of (\alpha \beta)_{ij} would have the general form: D \times \alpha_i \times \beta_j + E \times \alpha^2_i + F \times \beta^2_j.  Use this form to arrive at a proof by contradiction while enforcing the usual constraints on the interaction effects.