Question regarding groups

Hi I have a question here worth 17 marks in total. I am able to answer some of it however I am unsure where the marks are coming from:

a) State the definition of a group.

A group is a set with a binary operation which satisfies certain axioms.

A group must contain a set, binary operation and an identity element.

Im sure this might be worth 3 marks.

b) Suppose (G,~,e) is a group. Let a,b,c are elements of G and suppose that a~b=a~c

Prove that b=c stating where group axioms are being used.

All I can think of saying is that by the identity axiom and letting a=e on each side that infact b=c.

c) Suppose that n is a natural number and that A is a n x n matrix.

Set E(A)={X|X is ainvertible n x n matrix that commutes with A}

Prove that (E(A),.,I) is a group where . denotes matrix multiplication.

I would answer by the fact that by set definition X commutes with A so commutivity holds:

B and C are elements of E(A)

B.C=C.B

B, C and D are elements of E(A)

B.(C.D)=(B.C).D

And by identity axiom:

B is a element of E(A)

I.B=B=B.I

by multiplication by the identity matrix

Am I mostly correct?

I would appreciate any help or hints.

Cheers.