Question

Dada a matriz A abaixo:

Answer 1

Explicação passo-a-passo:

$\sf A^2=A\cdot A$

$\sf A^2=\left[\begin{array}{ccc} \sf 2&\sf -1&\sf 0 \\ \sf 1&\sf 0&\sf 0\\ \sf 0&\sf 0&\sf 1\end{array}\right]\cdot\left[\begin{array}{ccc} \sf 2&\sf -1&\sf 0 \\ \sf 1&\sf 0&\sf 0\\ \sf 0&\sf 0&\sf 1\end{array}\right]$

$\sf A^2=\left[\begin{array}{ccc} \sf 2\cdot2+(-1)\cdot1+0\cdot0&\sf 2\cdot(-1)+(-1)\cdot0+0\cdot0&\sf 2\cdot0+(-1)\cdot0+0\cdot1 \\ \sf 1\cdot2+0\cdot1+0\cdot0 &\sf 1\cdot(-1)+0\cdot0+0\cdot0 &\sf 1\cdot0+0\cdot0+0\cdot1 \\ \sf 0\cdot2+0\cdot1+1\cdot0 &\sf 0\cdot(-1)+0\cdot0+1\cdot0 &\sf 0\cdot0+0\cdot0+1\cdot1 \end{array}\right]$

$\sf A^2=\left[\begin{array}{ccc} \sf 4-1+0&\sf -2+0+0&\sf 0+0+0 \\ \sf 2+0+0&\sf -1+0+0&\sf 0+0+0\\ \sf 0+0+0&\sf 0+0+0&\sf 0+0+1\end{array}\right]$

$\sf A^2=\left[\begin{array}{ccc} \sf 3&\sf -2&\sf 0 \\ \sf 2&\sf -1&\sf 0\\ \sf 0&\sf 0&\sf 1\end{array}\right]$