Matrix multiplication proof

I have the following details about the matrices $A,B$:

$$A_{n\times n},B_{n\times n}$$ $$A^2 = B^2 = 0$$ $$AB=BA$$

I need to find $x \in \mathbb{N}$ so $(A+B)^x=0$

What implications can I make from the given details?

1. $A,B$ doesn't have to equal $0$ so $A^2 = B^2 = 0$
2. Can I imply from the 2nd and 3rd given details that $A=B$?
3. Any other leads?
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2
– bgins Apr 6 '12 at 11:42
Concering 2.: $B$ might be a scaled version of $A=\begin{pmatrix}0& 1\\0 &0\end{pmatrix}$, so no. – draks ... Apr 6 '12 at 11:49

1 Answer

For all $x \ge 3$, The equation $(A+B)^x=0$ is true because for $x =3$, it is true.

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