Jordan-block/2/Powers/Induction/Exercise

Let

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

with ${}\lambda \in K$. Show by induction that

${}M^{n}={\begin{pmatrix}\lambda ^{n}&n\lambda ^{n-1}\\0&\lambda ^{n}\end{pmatrix}}\,$

holds.

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