Characteristic polynomial/F2/10 00/Characteristic polynomial function is 0/Exercise

Let ${}K$ be the field with two elements, we consider the matrix

${}M={\begin{pmatrix}1&0\\0&0\end{pmatrix}}\,$

over ${}K$. Show that the characteristic polynomial ${}\chi _{M}$ is not the zero polynomial, but that

${}\chi _{M}(\lambda )=0\,$

holds for all ${}\lambda \in K$.

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