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Moderate

Determinant of a $2\times2$ Matrix

ACTMAT-ZEY8JE

If matrix $A$ is:

$$ \begin{bmatrix} 2x & 3 \\\ 4x & x \end{bmatrix} $$

...for which value(s) of $x$ does the determinant of $ A = -9$?

A

$ \cfrac{2}{3} \text{ only }$

B

$ -\cfrac{2}{3} \text{ only }$

C

$ -\cfrac{3}{2} \text{ only }$

D

$ \cfrac{3}{2} \text{ only }$

E

$ \cfrac{3}{2} \text{ and } -\cfrac{3}{2} $