Let $A = \left[\begin{array}{cc} 9 &1\cr -2 &6 \end{array}\right]$.
Find two different diagonal matrices $D$ and the corresponding matrix $S$ such that $A=SDS^{-1}$.

$D_1 =$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ 0 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ 0

$\quad S_1 =$

$\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$

.

$D_2 =$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ 0 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ 0

$\quad S_2 =$

$\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$

.