Show that the set is a vector space

Question

For a fixed m x n matrix $A$, show directly that the set {$b$|$Ax$ = $b$ is consistent} is a vector space.

1) It contains the zero vector

{o | $Ax$ = 0b is consistent}

2) it is closed under addition

let $b,d$ $\in$ col(A)

{$b+d$ | $Ax$ = $b+d$ is consistent} }

3) it is closed under multiplication

let c $\in$ $R$

{$cb$ | $Ax$ = $cb$ is consistent}}

are these steps the correct way to prove that the set {b|Ax = b is consistent} is a vector space?