Question Number 35626 by abdo mathsup 649 cc last updated on 21/May/18
$$\left.\mathrm{1}\right)\:{study}\:{the}\:{diagonalisstion}\:{of}\:{the}\:{matrice} \\ $$$${A}\:=\begin{pmatrix}{\mathrm{1}+{a}^{\mathrm{2}} \:\:\:\:\:{a}\:\:\:\:\:\:\:\mathrm{0}}\\{{a}\:\:\:\:\:\:\:\:\:\mathrm{1}+{a}^{\mathrm{2}} \:\:\:\:\:{a}}\end{pmatrix} \\ $$$$\:\:\:\:\:\:\:\:\:\:\left(\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:{a}\:\:\:\:\mathrm{1}+{a}^{\mathrm{2}} \:\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{A}^{{n}} \\ $$