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Question
If \[A = \begin{bmatrix}1 & 2 \\ 3 & - 1\end{bmatrix}\text{ and }B = \begin{bmatrix}1 & 0 \\ - 1 & 0\end{bmatrix}\] , find |AB|.
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Solution
\[A = \begin{bmatrix} 1 & 2\\3 & - 1 \end{bmatrix} \]
\[B = \begin{bmatrix} 1 & 0 \\ - 1 & 0 \end{bmatrix} \]
\[AB = \begin{bmatrix} 1 & 2\\3 & - 1 \end{bmatrix}\begin{bmatrix} 1 & 0\\ - 1 & 0 \end{bmatrix} = \begin{bmatrix}1 - 2 & 0 + 0 \\ 3 + 1 & 0 + 0\end{bmatrix} = \begin{bmatrix}- 1 & 0 \\ 4 & 0\end{bmatrix}\]
\[\left| AB \right| = 0 - 0 = 0\]
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