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Question
If \[A = \begin{bmatrix}1 & 2 \\ 3 & - 1\end{bmatrix}\text{ and B} = \begin{bmatrix}1 & - 4 \\ 3 & - 2\end{bmatrix},\text{ find }|AB|\]
Solution
\[A = \begin{bmatrix}1 & 2 \\ 3 & - 1\end{bmatrix}\]
\[ \Rightarrow \left| A \right| = - 1 - 6 = - 7\]
\[B = \begin{bmatrix}1 & - 4 \\ 3 & - 2\end{bmatrix}\]
\[ \Rightarrow \left| B \right| = - 2 + 12 = 10\]
\[\text{ If A and B are square matrices of the same order, then }\left| AB \right| = \left| A \right|\left| B \right| . \]
\[ \Rightarrow \left| AB \right| = \left| A \right|\left| B \right| = - 7 \times 10 = - 70\]
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