Question

Suppose |A| = 0, and that x1 is a particular solution of the system Ax = B. Show that any other solution x2 of this system can be written as x2 = x1 + x0, where x0 is a solution of the system Ax = 0

Answer 1

Ax1 = B
Ax2 = B
subtract these two.
Ax2-Ax1=B-B
Take A as common
A(x2-x1)=0
But its given that Ax0=0
Therefore equating, we have
x2-x1 = x0
Therefore x2 = x1 + x0.

I think i might be missing some subtle point in this proof.
I hope somebody goes through this solution and comments.