Inverse of augmented matrix

Assume upon using row operations the augmented matrix [Alb] can be reduced to
[1 0 0 ] -2 ]
[ 0 1 0 ] 3 ]
[ 0 0 0 ] 0 ]


Does A^-1 exist. If so, what is it. If A does not have an inverse, give a reason why not. How many equations does the system of equations Ax=b have?


Matrix A is first 3 columns. B is the last. There is a link below to view correctly.

If anybody could help I would be grateful.

http://i.imgur.com/gxfHa.png

A is not invertible. It it were, it would be row equivalent to the identity. That would mean that the last row would have to look like 0 0 1 (something).

The system Ax = b has infinitely many solutions. If the solution is x = (a, b, c), then a = -2, b = 3, and c is any real number.