Let V be an n-dimensional vector space where n>=1. If T : V -> V is a linear transformation, prove (a) => (b)
(a) im(T) = ker(T)
(b) T^2 = 0, n is even and r(T)=0.5n
I've got the T^2 = 0 bit. Unsure how the evenness of the dimension of the vector space comes into it.
Sorry, got the n is even bit now. I'll post again if I get stuck again.
Has yours come through yet?