$$A = \left[ {\matrix{ 1 & 2 \cr 0 & 1 \cr } } \right]$$ then by the principle of mathematical induction, prove that $${A^n} = \left[ {\matrix{ 1 & {2n} \cr 0 & 1 \cr } } \right]$$

Prove by induction that for all n $$\in$$ N, n² + n is an even integer (n $$\ge$$ 1).