2x2-matrix/Characteristic polynomial directly/Annihilation/Exercise

For a ${}2\times 2$-matrix ${}M={\begin{pmatrix}a&b\\c&d\end{pmatrix}}$, let

${}P_{M}:=X^{2}-\operatorname {trace} {\left(M\right)}X+\det M\,.$

Show that ${}P_{M}(M)=0$ holds.

Create a solution