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प्रश्न
If A and B are square matrices of the same order such that |A| = 3 and AB = I, then write the value of |B|.
उत्तर
Since A & B are square matrices of the same order, by the property of determinants we get
\[\left| AB \right| = \left| A \right| \times \left| B \right|\]
\[\left| A \right| = 3, AB = I \]
\[ \Rightarrow \left| AB \right| = 1\]
\[ \Rightarrow \left| A \right| \times \left| B \right| = 1\]
\[3 \times \left| B \right| = 1\]
\[\left| B \right| = \frac{1}{3}\]
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