If P is a 3 × 3 matrix such that P T = 2 P + I , where P T is the transpose of P and I is…
Mathematics · JEE Advanced · NTA Exams — Matrices and Determinants
If P is a 3 × 3 matrix such that PT = 2P + I, where PT is the transpose of P and I is the 3 × 3 identity matrix, then there exists a column matrix \[X=\left[\begin{array}{l}
x \\
y \\
z
\end{array}\right] \neq\left[\begin{array}{l}
0 \\
0 \\
0
\end{array}\right]\] such that
- PX = X
- PX = 2X
- PX = – X
Answer
(D) PX = – X
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