Problem with two matrix – math.stackexchange.com

Let $A,B \in M_n(C) $. The matrix $A-B$ is invertible and $(A+B)^k=A^k+B^k $, $k \in {2,3} $. Prove that $(A+B)^m=A^m+B^m $ for every $m \in N $. PS. I obtained $AB+BA=0$ and $A^2B+B^2A=0$, but I ...

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