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## Main Question or Discussion Point

If [tex]X\in\textrm{End}(\mathbb{R}^n)[/tex] is some arbitrary nxn-matrix, is it true that

[tex]

X^2 = 0\quad\implies\quad \textrm{Tr}(X)=0?

[/tex]

[tex]

X^2 = 0\quad\implies\quad \textrm{Tr}(X)=0?

[/tex]