Proof involving matrix equation $A$ and $B$ are $(n\times n)$ matrices and $AB + B + A = 0$. Prove that then $AB=BA$.
How should I approach this problem?

Adding the identity matrix $I$ on both sides, we find $(A+I)(B+I) = I$. Hence $A+I$ and $B+I$ are inverses of each other. It follows that $(B+I)(A+I) = I$ as well. Expanding gives $BA + B + A = 0$, hence $AB = BA$.
