Let $A,B$ be square real matrices of the same size such that $A+B=AB$. Show that $AB=BA$.
I have got the result for invertible matrices, but what about non-invertible ones?
Asked
Active
Viewed 133 times
0
Parcly Taxel
- 103,344
-
From the given condition I am getting (A+B)=BA – nandita mukherjee Mar 01 '18 at 05:04
-
By using invertibility – nandita mukherjee Mar 01 '18 at 05:04
-
2This does NOT follow. We aren't merely defining $AB=A+B$ ... it just happens that they are equal. This is not a matter of mere symbol manipulation. – Squirtle Mar 01 '18 at 05:11
-
Nandita , you've got your answer , I think , If you've any doubt you may comment . – Learning Mar 01 '18 at 05:24
-
Ok thanks but can you please explain the fact that if A and B are taken to be invertible then what will happen – nandita mukherjee Mar 01 '18 at 05:26
-
https://math.stackexchange.com/a/2242650/516174 , In this answer $A$ and $B$ are general matrices they can be singular or non-singular. Also, see my comments below this answer . – Learning Mar 01 '18 at 05:32