Question

设abc均为n阶方阵,b=e+ab

线性代数，求大神帮忙～
设abc均为n阶矩阵，E为单位矩阵，若B=E+AB,C=A+CA,则B-C=
要详细步骤，谢谢啦～

Answer 1

简单计算一下即可，答案如图所示

Answer 2

B = E+AB ， (E-A)B = E,
则 E-A, B 均可逆，B = (E-A)^(-1), E-A = B^(-1);
C = A+CA, C(E-A) = A, CB^(-1) = A, C = AB
得 B-C = B-AB = E