Question

se a= $\left[\begin{array}{ccc}3&1\\4&8\end{array}\right]$ e b= -$\left[\begin{array}{ccc}-1&2\\-2&6\end{array}\right]$, determine: det (ab)

Answer 1

Olá GabbieSun, boa tarde!

 Uma vez que as matrizes são quadradas e possuem a mesma ordem, podemos aplicar o teorema de Binet.

 A saber, $\mathbf{\det (A \cdot B) = \det A \cdot \det B}$.


 Isto posto,

$\\ \mathsf{\det (A \cdot B) = \det A \cdot \det B} \\\\ \mathsf{\det (A \cdot B) = (3 \cdot 8 - 4 \cdot 1) \cdot [(- 1) \cdot 6 - (- 2) \cdot 2]} \\\\ \mathsf{\det(A \cdot B) = (24 - 4) \cdot (- 6 + 4)} \\\\ \mathsf{\det(A \cdot B) = 20 \cdot - 2} \\\\ \boxed{\mathsf{\det(A \cdot B) = - 40}}$