Question

07 - Observe a matriz :
A matriz M² = M x M é:
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Answer 1

Se M² = M × M, então:

$M^2=\left[\begin{array}{cc}\!\!-1&2\\\!\!-2&3\end{array}\right]\times\left[\begin{array}{cc}\!\!-1&2\\\!\!-2&3\end{array}\right]$

$M^2=\left[\begin{array}{cc}\!\!-1\times(-\,1)+2\times(-\,2)&\!\!-1\times2+2\times3\\\!\!-2\times(-\,1)+3\times(-\,2)&\!\!-2\times2+3\times3\end{array}\right]$

$M^2=\left[\begin{array}{cc}1+(-\,4)&\!\!-2+6\\2+(-\,6)&\!\!-4+9\end{array}\right]$

$M^2=\left[\begin{array}{cc}1-4&4\\2-6&5\end{array}\right]$

$M^2=\left[\begin{array}{cc}\!\!-3&4\\\!\!-4&5\end{array}\right]$

(Basta multiplicar as linhas da primeira matriz pelas colunas da segunda matriz e sempre somar após multiplicar os elementos).

Bons estudos e um forte abraço. — lordCzarnian9635.