How do you multiply determinants?

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Solution

Suppose we have two $2 \times 2$ matrices, whose determinants are given by:
$∆_{1} = | \begin{matrix} a_{1} & b_{1} \\ a_{2} & b_{2} \end{matrix} | ∆_{2} = | \begin{matrix} c_{1} & d_{1} \\ c_{2} & d_{2} \end{matrix} | ∆_{1} = a_{1} b_{2} - a_{2} b_{1} ∆_{2} = c_{1} d_{2} - c_{2} d_{1}$
Now multiply $∆_{1} a n d ∆_{2}$
$∆_{1} ∆_{2} = (a_{1} b_{2} - a_{2} b_{1}) (c_{1} d_{2} - c_{2} d_{1})$

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How do you multiply determinants?

Suppose we have two 2×2 matrices, whose determinants are given by:∆1=|a1b1a2b2|∆2=|c1d1c2d2|∆1=a1b2-a2b1∆2=c1d2-c2d1Now multiply ∆1and∆2∆1∆2=(a1b2-a2b1)(c1d2-c2d1)