I have this following problem:
let $0\neq A\in M_n(F)$ such that $A^k=0$ for integer $k>1$
a. what are the eigenvalues of A?
b. show that $B=\alpha\cdot I_n-A$ invertible for every scalar $\alpha\in F, \alpha \neq0.$
I know that the answer for a is that zero is the only eigenvalue but I dont know how to explain it well.
and I dont have a clue for b.