Let P=-302056901401121206014 and A=27ω2-1-ω10-ω-ω+1 where ω=-1+i32, and I3 be the  identity matrix of order 3 . If the determinant of the matrix P-1AP-I32 is αω2, then the  value of α is equal to

P-1AP-I2=P-1AP-P-1P2=P-1(A-I)P2=P-12|A-I|2|P|2  =|A-I|2                               A−I=17ω2−1−ω−110−ω−ω                                                                    =17ω20−ω−61+ω20−ω−ω                 · R2→R2+R1                              =ωω+6+ω1+ω2                        =ω1+ω2+ω+6=6ω∴A−I2=36ω2