Let P = √3/2 1/2 -1/2 √3/2, A = 1 1 0 1, and Q = PAP^T. If P^TQ²⁰… | JEE Main 2023 Mathematics PYQ

MCQMediumJEE Main 2023 · 8 April, Shift 1Algebra of Matrices

Let $P = \begin{bmatrix} \frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2} \end{bmatrix}$ , $A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$ , and $Q = PAP^T$ . If $P^TQ^{2007}P = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$ , then $2a + b - 3c - 4d$ equals:

A
$2004$
B
$2007$
C
$2005$
D
$2006$

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