If $P$ is a $3 \times 3$ real matrix such that $P^T=a P+(a-1) I$, where $a1$, then [JEE Main 2023, 30 Jan (Shift 2)]

Question

If $P$ is a $3 \times 3$ real matrix such that $P^T=a P+(a-1) I$, where $a>1$, then [JEE Main 2023, 30 Jan (Shift 2)]

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If \(P\) is a \(3 \times 3\) real matrix such that \(P^T=a P+(a-1) I\), where \(a>1\), then [JEE Main 2023, 30 Jan (S…