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I have a continuous curve $A:\mathbf{R}_+\rightarrow \text{M}_N(\mathbf{R})$ such that $[A(t),A(s)] \operatorname*{\longrightarrow}_{t,s\rightarrow +\infty} 0$, where $[A(t),A(s)] = A(t)A(s)-A(s)A(t)$....