A,B为n阶矩阵且A+B=E,证明AB=BA
问题描述:
A,B为n阶矩阵且A+B=E,证明AB=BA
答
A(A+B)=AA+AB (A+B)A=AA+BA AA+AB=A=AA+BA 所以AB=BA
A,B为n阶矩阵且A+B=E,证明AB=BA
A(A+B)=AA+AB (A+B)A=AA+BA AA+AB=A=AA+BA 所以AB=BA