Help with commutative property of matrices problem Given matrices $A$ and $B$, where that $AB = A + B$, prove $AB = BA$.
I keep coming up with AB = AB. It seems like basic algebra, but for the life of me, I'm getting nowhere :/. Someone help please?
Hint: Consider $(A-I)(B-I)$, where $I$ is the identity matrix.
The following must apply simultaneously
$$AB+A+B=0$$
$$BA+B+A=0$$
Subtract the two equations and get the assumption.