JEE PYQ: Matrices And Determinants Question 39
Question 39 - 2020 (04 Sep Shift 1)
If $A = \begin{bmatrix} \cos\theta & i\sin\theta \ i\sin\theta & \cos\theta \end{bmatrix}$, $\left(\theta = \dfrac{\pi}{24}\right)$ and $A^5 = \begin{bmatrix} a & b \ c & d \end{bmatrix}$, where $i = \sqrt{-1}$, then which one of the following is not true?
(1) $0 \leq a^2 + b^2 \leq 1$
(2) $a^2 - d^2 = 0$
(3) $a^2 - c^2 = 1$
(4) $a^2 - b^2 = \dfrac{1}{2}$