Direct sums and injective, projective, flat

Let R be a commutative ring (with unity) and let M1 and M2 be two R-modules. Prove that M1βŠ•M2 is:

  1. projective if and only if both M1 and M2 are projective
  2. injective if and only if both M1 and M2 are both injective
  3. flat if and only if both M1 and M2 are flat