Question

设n阶方阵A满足A^2=En 且 |A+En|不等于0,证明：A=En

Answer 1

A^2=AA=E===> A=A'=A^(-1)=A^* 并且A不为0或(-E)

因为E^2=E

===>A^2-E^2=0

===> (A+E)(A-E)=0

---> A=E

To your question:

If AB=0, and A has left invert, then B=0.

Because A^(-1)AB=A^(-1) 0=0 ====>B=0