Let P=[\table -30 , 20 , 56 ; 90 , 140 , 112 ; 120 , 60 , 14] and A=[\table 2 , 7 , \omega^{2} ; -1 , -\omega , 1 ; 0 , -\omega , -\omega+1] where, \omega=\frac{-1+i \sqrt{3}{2}, and I_{3} be the identity matrix of order 3 . If the determinant of the matrix (P^{-1} A P-I_{3})^{2} is \alpha \omega^{2}, then the value of \alpha is equal to......... [16 Mar 2021 Shift 1]

JEE Main 16 March 2021 Shift 1 Solved Paper

Section: Mathematics

Question : 86 of 90

Marks: +1, -0

Let P=[

] and A=[

]
where, ω=‌

−1+i√3

, and I3 be the identity matrix of order 3 . If the determinant of the matrix (P−1AP−I3)2 is αω2, then the value of α is equal to.........

[16 Mar 2021 Shift 1]

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