# Properties of the Determinant I

Algebra Level 3

The determinant has the properties:

$$\det(AB) = \det(A)\det(B) \\ \det(A) = \det(A^T)$$

Hence, given that $$\begin{vmatrix} a_1 & a_2 & a_3 \\ a_4 & a_5 & a_6 \\ a_7 & a_8 & a_9 \\ \end{vmatrix} = 16$$

Find $$\begin{vmatrix} 4a_1 & 2a_2 & 4a_3 \\ 2a_4 & a_5 & 2a_6 \\ 4a_7 & 2a_8 & 4a_9 \\ \end{vmatrix}$$

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