let f: V--> W. if the dim V = dim W, prove that f might not be an isomorphism.
in this case, if the dimV= rank f + nullity f= dim W,
it means that nullity f = 0.
for f to be an isomorphism, it means that it is bijective and linear.
so in this case, we need to prove that it is not linear.
let f(x) = (x)^2 + 1. then its proven.
can it be done like this?