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Question
If A and B are square matrices of order 3 such that |A| = –1, |B| = 3, then find the value of |2AB|.
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Solution
\[\left| K A \right| = K^n \left| A \right| \left[ \text { n is the order of A } \right]\]
\[ \Rightarrow \left| 2AB \right| = 2^3 \left| AB \right| . . . (1)\]
\[\text { If A and B are square matrices of the same order, then } \left| AB \right| = \left| A \right| \left| B \right| . So, \]
\[\left| 2AB \right| = 2^3 \left| A \right| \left| B \right| \left[ \text { From } (1) \right]\]
\[ = 8 \times - 1 \times 3\]
\[ = - 24\]
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