Unique solution & Matrix multiplication

[camchatwebcam]

If the equation Ax = b has at least one solution for each b in Rn, then the solution is unique for each b.
is true...

 

[blamocur]

Is A a sqare matrix?

 

[Steven G]

That statement is simply not true.
Assume A is square.
If A^-1 exists, then there there are how many solutions?
If A^-1 does not exists, then there are how many solutions?