I have a linear operator defined by three linear equations, and I need to determine whether the operator is one to one and/or onto...

The standard matrix of this is:

1 2 3
2 5 3
1 0 8

How do I figure out whether the operator is 1-1 or onto?

A further question, how does one find a reflection of a matrix across y=-x of a 2X2 matrix? (generally speaking)