JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If \(A\) is a \(3\times3\) matrix such that \(\left| {5.adjA} \right| = 5\), then \(\left| A \right|\) is equal to
- A \( \pm \frac{1}{5}\)
- B \( \pm \frac{1}{25}\)
- C \( \pm 1\)
- D \( \pm 5\)
Answer & Solution
Correct Answer
(A) \( \pm \frac{1}{5}\)
Step-by-step Solution
Detailed explanation
\(\left| {5\,.adj\,A} \right| = 5 \Rightarrow {5^3}.{\left| A \right|^{3 - 1}} = 5\) \( \Rightarrow 125{\left| A \right|^2} = 5 \Rightarrow \left| A \right| = \pm \frac{1}{5}\)
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