JEE PYQ: Matrices And Determinants Question 3
Question 3 - 2021 (16 Mar Shift 1)
Let $P = \begin{bmatrix} -30 & 20 & 56 \ 90 & 140 & 112 \ 120 & 60 & 14 \end{bmatrix}$ and $A = \begin{bmatrix} 2 & 7 & \omega^2 \ -1 & -\omega & 1 \ 0 & -\omega & -\omega + 1 \end{bmatrix}$
where $\omega = \dfrac{-1 + i\sqrt{3}}{2}$, and $I_3$ be the identity matrix of order 3. If the determinant of the matrix $(P^{-1}AP - I_3)^2$ is $\alpha\omega^2$, then the value of $\alpha$ is equal to ______.
BETA
