If A = \(\begin{bmatrix}4 & 10\\2 & 1 \end{bmatrix}\), then what is the value of |\(3 { A }^{ T } \)|?
Answer & explanation
Correct answer: option 4
If Matrix A has size a × a and k is a constant, then |kA| = \( { k }^{ a } \) |A|
Then, |\(3 { A }^{ T } \)| = \( { 3 }^{ 2 } \) |\( { A }^{ T } \)|
= \( { 3 }^{ 2 } \) |A |
Because |\( { A }^{ T } \) = |A |
|\(3 { A }^{ T } \)| = 9 |A |
And |A | = -16
So, |\(3 { A }^{ T } \)| = -144