JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If \(P\) is a \(3 \times 3\) real matrix such that \(P ^{ T }=a P +( a -1) I\), where \(a > 1\), then \(..........\)
- A \(P\) is a singular matrix
- B \(|\operatorname{Adj} P|>1\)
- C \(|\operatorname{Adj} P|=\frac{1}{2}\)
- D \(|\operatorname{Adj} P|=1\)
Answer & Solution
Correct Answer
(D) \(|\operatorname{Adj} P|=1\)
Step-by-step Solution
Detailed explanation
\(P ^{ T }= aP +( a -1) I\) \(\Rightarrow P = aP ^{ T }+( a -1) I\) \(\Rightarrow P ^{ T }- P = a \left( P - P ^{ T }\right)\) \(\Rightarrow P = P ^{ T } \text {, as } a \neq-1\) \(\text { Now, } P = aP +( a -1) I\) \(\Rightarrow P =- I \Rightarrow| P |=1\)…
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