线性代数证明题 求高手指教！！Let A be an n × n matrix such that An = 0 but

线性代数证明题 求高手指教！！
Let A be an n × n matrix such that An = 0 but An− 1 = 0.
(1) Prove that there exists a basis B = (v1, . . . ,vn) of Rn such that Avi = vi+1 for i < n and Avn = 0.
(2) Find the rank of An− 1.
(3) Find the rank of A.
(4) A square matrix B is called nilpotent if Bm = 0 for some m ∈ N. Prove that if B is a nilpotent n × n matrix, then Bn = 0.
第一行条件因该是A(n-1) 不等于 0
第二问的也是A(n-1)
不好意思打错了。。。