Answer
$det\:\left(A\right)=-126$
Work Step by Step
$Using\:the\:following\:method\:described\:in\:the\:book\:for\:example\:5\\We\:have\:needed\:to\:compute\:the\:diagonal\:products\\\:\begin{bmatrix}3&8&-7\\ 0&-5&4\\ 8&1&6\:\:\:\end{bmatrix}\:\:\begin{bmatrix}3&8\\ 0&-5\\ 8&1\:\:\:\end{bmatrix}\\Now\:we\:can\:compute\:the\:determinant\\det\:\left(A\right)=\left(-5\cdot 3\cdot 6+8\cdot 4\cdot 8-7\cdot 0\cdot 1\right)-\left(8\cdot 5\cdot 7+1\cdot 4\cdot 3+6\cdot 0\cdot 8\right)\\=-90+256-0-280-12-0\\=256-382\\det\:\left(A\right)=-126$
