Resposta:
16
Explicação passo a passo:
[tex]A^{2}=\left[\begin{array}{cc}2&0\\0&-2\\\end{array}\right]\cdot\left[\begin{array}{cc}2&0\\0&-2\\\end{array}\right]=\left[\begin{array}{cc}4&0\\0&4\\\end{array}\right][/tex]
[tex]2A^{2}=2\cdot\left[\begin{array}{cc}4&0\\0&4\\\end{array}\right]=\left[\begin{array}{cc}8&0\\0&8\\\end{array}\right][/tex]
[tex]B^{2}=\left[\begin{array}{cc}0&-1\\1&0\\\end{array}\right]\cdot\left[\begin{array}{cc}0&-1\\1&0\\\end{array}\right]=\left[\begin{array}{cc}-1&0\\0&-1\\\end{array}\right][/tex]
[tex]4B^{2}=4\cdot\left[\begin{array}{cc}-1&0\\0&-1\\\end{array}\right]=\left[\begin{array}{cc}-4&0\\0&-4\\\end{array}\right][/tex]
[tex]2A^{2}+4B^{2}=\left[\begin{array}{cc}8&0\\0&8\\\end{array}\right]+\left[\begin{array}{cc}-4&0\\0&-4\\\end{array}\right]=\left[\begin{array}{cc}4&0\\0&4\\\end{array}\right][/tex]
O produto dos números presentes na diagonal principal é 4 · 4 = 16.
