Jordan-block/2/Powers/Induction/Exercise

Let

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

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

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

holds.