Let P=⎡⎢⎣−302056901401121206014⎤⎥⎦ and A=⎡⎢⎣27ω2−1−ω10−ω−ω+1⎤⎥⎦ where ω=−1+i√32 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

Let P=⎡⎢⎣−302056901401121206014⎤⎥⎦ and A=⎡⎢⎣27ω2�

1.	Let P=⎡⎢⎣−302056901401121206014⎤⎥⎦ and A=⎡⎢⎣27ω2−1−ω10−ω−ω+1⎤⎥⎦ where ω=−1+i√32 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
Answer» Let $P = ⎡ ⎢ ⎣ \begin{matrix} - 30 & 20 & 56 90 & 140 & 112 120 & 60 & 14 \end{matrix} ⎤ ⎥ ⎦$ and $A = ⎡ ⎢ ⎣ \begin{matrix} 2 & 7 & ω^{2} - 1 & - ω & 1 0 & - ω & - ω + 1 \end{matrix} ⎤ ⎥ ⎦$ where $ω = \frac{- 1 + i \sqrt{3}}{2}$ and $I_{3}$ be the identity matrix of order 3. If the determinant of the matrix $(P^{- 1} A P - I_{3})^{2}$ is $α ω^{2}$ , then the value of $α$ is equal to