Question
Evaluate the following $ :\left|\begin{array}{cc} -2 & 3 \\ -1 & 4 \end{array}\right|\left|\begin{array}{cc} 6 & 4 \\ 3 & -1 \end{array}\right| $
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Answer
$\begin{array}{l}\left|\begin{array}{cc}-2 & 3 \\ -1 & 4\end{array}\right|_{2 \times 2}\left|\begin{array}{cc}6 & 4 \\ 3 & -1\end{array}\right|_{2 \times 2} \end{array} $
$ =\left|\begin{array}{cc}-2 \times 6+3 \times 3 & -8-3 \\ -6+4 \times 3 & -4-4\end{array}\right| $
$ =\left|\begin{array}{cc}-3 & -11 \\ 6 & -8\end{array}\right|_{2 \times 2}$
$ =\left|\begin{array}{cc}-2 \times 6+3 \times 3 & -8-3 \\ -6+4 \times 3 & -4-4\end{array}\right| $
$ =\left|\begin{array}{cc}-3 & -11 \\ 6 & -8\end{array}\right|_{2 \times 2}$
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