How to determine if a function is simple in linear algebra?

Question

V = { (x, y, z) in R³ : x + y - z = 0 } and f : R³ ---> R³

V = Ker(f) and  1 is an eigenvalue of f .

How can I determine if f is simple or not ?

And also how can I find the dimension of the Kernel of f ; and the dimension of the Image of f ?

Thank you so much for the help

Answer 1