Question

线性代数设A’B均为n阶矩阵’且AB=A+B’证明A’B可交换'

Answer 1

证明:由 AB=A+B

得 (A-I)(B-I) = AB-A-B+I = I

所以 A-I 可逆,且 I = (B-I)(A-I) = BA-B-A+I

所以 BA = A+B = AB.