It is known that the linear equation AX = B has two different solutions X1 and x2. There must be innumerable solutions to prove this equation

It is known that the linear equation AX = B has two different solutions X1 and x2. There must be innumerable solutions to prove this equation

x=x1,x=x2
Then ax1 = b
ax2=b
subtract
a(x1-x2)=0
Because x1, X2 are two different solutions
So x1-x2 ≠ 0
So a = 0
Then B = ax1 = 0
So AX = B has innumerable solutions