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I need to prove the following statement for all matrices A, B:

$$A_{n \times n}, B_{n \times n} \text{ over } \mathbb{R}$$ $$BA = 0_{n \times n} \implies (AB)^2 = 0_{n \times n}$$

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

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