If SE L(R) is the stretching transformation S(x, y) = (3x, 3y) and TEL(R) is of...

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If SE L(R²) is the stretching transformation S(x, y) = (3x, 3y) and TEL(R²) is of the form T(x, y) = (3x + 2y, 4x - 3y), do S and T commute (i.e. do we have ST = TS)? If SE L(R³) is the stretching transformation S(x, y, z) = (3x, 3y, 3z) and TEL(R³, R²) is of the projection transformation T(x, y, z) = (x, y), do S and T commute? If T, SE L(P₂, P4) are of the form (Tp)(x) = p(x²), (Sp)(x) = r²p(x), do S and T commute? In parts (a-c) above, what are N(ST), N(TS), R(ST) and R(TS) (when they are defined)? If SE L(R²) is the stretching transformation S(x, y) = (3x, 3y) and TEL(R²) is of the form T(x, y) = (3x + 2y, 4x - 3y), do S and T commute (i.e. do we have ST = TS)? If SE L(R³) is the stretching transformation S(x, y, z) = (3x, 3y, 3z) and TEL(R³, R²) is of the projection transformation T(x, y, z) = (x, y), do S and T commute? If T, SE L(P₂, P4) are of the form (Tp)(x) = p(x²), (Sp)(x) = r²p(x), do S and T commute? In parts (a-c) above, what are N(ST), N(TS), R(ST) and R(TS) (when they are defined)?