已知3阶矩阵A有3维向量A满足A^3X=3AX-A^2X,且向量组X,AX,A^2X线性无关.（1）记P=(X,AX,A^2X),求三阶矩阵B

1)AP=A(x, Ax, A^2*x)
=(AX,A^2X,A^3X)
=(AX,A^2X,3AX-A^2X)
=(X,AX,A^2X)[ 0 00
1 0 3
01 -1 ]
=PB
B =[ 0 00
1 0 3
01 -1 ]
2)AP=PB ,X,AX,A^2X线性无关,P可逆
P逆*A*P=B ,A与B相似
|A|=|B|=0