I am studying linear algebra about matrix multiplication, addition, subtraction, and inverses. I came across this question that I have the book solution to, but my own solution is slightly different. I need your feedback about few steps that I am confused about, please go to "My Question" section.
Given the following matrices,
find matrix X if any that satisfies the equation BX + AB = CX.
Notice the book solutions says the answer is (C - B)^-1 * AB, but my answer is AB * (C - B)^-1. I have calculated the result, and the answer is different. Could you please explain what am I doing wrong? Why does the book says (C - B)^-1 * AB is the answer?