A,B是方阵(AB)^2=A^2+AB+BA+B^2,A^2=A,B^2=B,求证AB=0
问题描述：
A,B是方阵(AB)^2=A^2+AB+BA+B^2,A^2=A,B^2=B,求证AB=0
答
(ab)^2=a^2+2ab+b^2=(a+b)^2
∵a^2=a∴a=1ora=0同理:b=1orb=0
∵(ab)^2=(a+b)^2∴a=0,b=0
∴ab=0