Some easy problems for warm-up

[lime]

Let A be the set of 2x2 matrices.
Let B be the set of matrices {X in A: MX = XM}, where M = [1 1; 0 1] matrix.

Which of the following must be true?

I. P, Q are in B -> P+Q is in B;
II. P, Q are in B -> PQ is in B.
III. B is a subgroup of GL(2), (under addition).
IV. B is a ring.
V. B is a field.
VI. For every X in B follows X^-1 = X^T.