Linear endomorphism/R^2/Characteristic polynomial/Eigenvalue/Exercise

Show that ${}\lambda \in K$ is an eigenvalue for the linear mapping

$\varphi \colon K^{2}\longrightarrow K^{2}$

given by a matrix of the form ${}{\begin{pmatrix}a&b\\c&d\end{pmatrix}}$ if and only if ${}\lambda$ is a zero of the polynomial

$X^{2}-(a+d)X+ad-cb.$

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