设A,B为N阶方阵,且A=1⼀2(B+E),证明A^2=A,当且仅当B^2=E

2025-01-07 01:07:43
推荐回答(2个)
回答1:

A^2=[1/2(B+E)]^2
=1/4(B^2+2B+E)=A=1/2(B+E)
化简得
B^2=E

回答2:

∵A²=1/4*(B²+2B+E)=B²/4+B/2+E/4=B/2+E/2
∴B²/4=E/4
即B²=E