For what value of x will |\( -2 { A }^{ T } \)| =20 if A = \(\begin{bmatrix}x & 4\\3 & 1 \end{bmatrix}\)?

17 -1 0 2

17

Given that |-2\( { A }^{ T } \)| =20 Also,   \((-2)^{ 2 } \) |\( { A }^{ T } \)| 4|\( { A }^{ T } \)| = 20 Because |\( { A }^{ T }| \) = |A | So, 20 = 4|A| 20= 4(x-12) 5=x-12 17=x