Answer to Question #206960 in Linear Algebra for Blackvey

Question

Find det(-2A) and compare it to det(A) for A=[-2 1 3][1 4 5][2 3 1]

Answer 1

$det(A)=\begin{vmatrix} -2 & 1&3 \\ 1 & 4&5\\ 2&3&1 \end{vmatrix}=2\cdot11+9-3\cdot5=16$

$det(-2A)=\begin{vmatrix} 4 & -2&-6 \\ -2 & -8&-10\\ -4&-6&-2 \end{vmatrix}=-4\cdot44-2\cdot36+6\cdot20=-128$

$det(2A)=-8det(A)$