For matrices $A, B$, show that $BA = 0 \Rightarrow (AB)^2 = 0$ I need to prove the following statement for all matrices A, B:
$$A_{n \times n}, B_{n \times n} \text{ over } \mathbb{R}$$
$$BA = 0_{n \times n} \implies (AB)^2 = 0_{n \times n}$$

$(AB)^2=AB.AB=A(BA)B=0$ since $BA=0$
