What is the determinant of the matrix $\begin{bmatrix} 10 & 8 \\ 20 & 12 \end{bmatrix}$ ?

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The determinant of a two by two matrix:

$$\text{det}\begin{bmatrix} a & b \\ c & d \end{bmatrix} = ad-bc$$ $$\text{det}\begin{bmatrix} 10 & 8 \\ 20 & 12 \end{bmatrix} = 10\cdot12 - 8\cdot 20$$ $$= 120-160 = \boxed{-40}$$

Determinants can be calculated using your calculator. The instructions for each type of calculator varies.