简答题:设A为二阶矩阵，P=(，A)，其中是非零向量且不是A的特征向量．
(I)证明P为可逆矩阵；
(Ⅱ)若A²+A-6=0，求P^-1AP，并判断A是否相似于对角矩阵．

A <img width="117" height="41" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232647_7101.jpg" /> B <img width="143" height="42" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232648_8351.jpg" /> C <img width="99" height="44" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232649_8721.jpg" /> D <img width="143" height="44" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232650_9601.jpg" />

A <img width="385" height="49" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232653_1163.jpg" /> B <img width="361" height="43" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232654_1632.jpg" /> C <img width="394" height="49" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232655_2569.jpg" /> D <img width="361" height="43" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232656_3819.jpg" />

A <img width="358" height="51" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232658_5070.jpg" /> B <img width="363" height="51" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232659_6944.jpg" /> C <img width="357" height="52" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232700_6320.jpg" /> D <img width="362" height="52" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232702_1789.jpg" />

A <img width="258" height="47" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232704_3038.jpg" /> B <img width="258" height="48" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232704_9288.jpg" /> C <img width="263" height="48" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232706_4132.jpg" /> D <img width="263" height="47" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232707_0684.jpg" />

A 存在矩阵P，使得PA=B B 存在矩阵P，使得BP=A C 存在矩阵P，使得PB=A D 方程组Ax=0与Bx=0同解

A <img width="28" height="34" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232710_7100.gif" />可由<img width="30" height="34" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232711_3351.gif" />，<img width="30" height="36" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232712_8507.gif" />线性表示 B <img width="30" height="34" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232711_3351.gif" />可由<img width="28" height="34" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232710_7100.gif" />，<img width="30" height="36" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232712_8507.gif" />线性表示 C <img width="30" height="36" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232712_8507.gif" />可由<img width="28" height="34" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232710_7100.gif" />，<img width="30" height="34" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232711_3351.gif" />线性表示 D <img width="28" height="34" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232710_7100.gif" />，<img width="30" height="34" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232711_3351.gif" />，<img width="30" height="36" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232712_8507.gif" />线性无关

A <img width="24" height="62" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232714_9844.gif" /> B <img width="24" height="62" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232715_6319.gif" /> C <img width="24" height="62" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232717_1475.gif" /> D <img width="32" height="62" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232717_9795.gif" />

A 1-<img width="26" height="24" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232719_2569.gif" />(1) B <img width="26" height="24" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232719_2569.gif" />(1) C 1-<img width="26" height="24" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232719_2569.gif" />(0．2) D <img width="26" height="24" src="https://www.beizhujiaoyu.com/uploads/202208/20210427232719_2569.gif" />(0．2)