(16%) Consider ordered pairs from R2 and define addition as: (21, X2) + (91, y2) = (x1 + 291, 12 + 242) and scalar multiplication as: a($1, T2) = (2021, QX2) Show your work for each of the following. (a) Does the above satisfy commutativety of addition: a ty = y +x? (b) Does the above satisfy associativity of addition: (x ty) + z = x + (y + z)? (c) Identity element of addition: 3B E R2 so that Vx, x + 8 = x? (d) Does it satisfy the distributive law for scalar multiplication: Vo ER, a(x ty) = ar tay? (e) Identity element of multiplication: Fo E R so that Vr, ax = x