WBJEE · Maths · Determinants
Let \(I\) denote the \(3 \times 3\) identity matrix and \(P\) be a matrix obtained by rearranging the columns of
\(I\). Then,
- A there are six distinct choices for \(P\) and \(\operatorname{det}(P)=1\)
- B there are six distinct choices for \(P\) and \(\operatorname{det}(P)=\pm 1\)
- C there are more than one choices for \(P\) and some of them are not invertible
- D there are more than one choices for \(P\) and \(P^{-1}=1\) in each choice
Answer & Solution
Correct Answer
(B) there are six distinct choices for \(P\) and \(\operatorname{det}(P)=\pm 1\)
Step-by-step Solution
Detailed explanation
Given, \(I=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]\) Then, \(\quad \operatorname{det}(I)=1\) If we take \(I\) as \[ A_{1}=\left[\begin{array}{lll} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{array}\right] \] Then,…
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