Let (0, ) and A= [ array lll 1 & 2 & 1 & 0 & 1 0 & 1 & 2 array ] . If det ( adj (2 A-A^T ) adj (A-2 A^T ) )=2^8 , then ( det (A))^2 is equal to:

Step-by-step solution

aligned & | adj ( A -2 ~A ^ T ) (2 ~A - A ^ T ) |=28 & | ( ~A -2 ~A ^ T ) (2 ~A - A ^ T ) |=24 & | ~A -2 ~A ^ T | |2 ~A - A ^ T |= 16 & ( ~A -2 ~A ^ T )^ T = A ^ T -2 ~A & | ~A -2 ~A ^ T |= | A ^ T -2 ~A | & | A -2 ~A ^ T |^2=16 & | ~A -2 ~A ^ T |= 4 & [ array ccc 1 & 2 & 1 & 0 & 1 0 & 1 & 2 array ]- [ array ccc 2 & 2 & 0 4 & 0 & 2 2 & 2 & 4 array ] & | array lll -1 & 0 & -3 & 0 & -1 -2 & -1 & -2 array | & 1+3 =4 & 3 =3 & =1 & | ~A |= | array lll 1 & 2 & 1 1 & 0 & 1 0 & 1 & 2 array |=-1-3=-4 & | ~A |^2=16 aligned