If A is a square matrix of order 3 such that det (A)=3 and det ( adj (-4 adj (-3 adj (3 adj ((2 ~A )⁻¹ ) ) ) ) )=2^ m 3^ n , then m +2 n is equal to :

Step-by-step solution

aligned & | A |=3 & adj (-4 adj (-3 adj (3 adj ((2 ~A )⁻¹ ) ) ) . & -4 adj (- .3 adj (3 adj (2 ~A )⁻¹ ) |^2 . & 4^6 | adj (-3 adj (3 adj (2 ~A )⁻¹ ) ) |^2 & 2¹² 3¹² |3 adj (2 ~A )⁻¹ |^8 & 2¹² 3¹² 3²⁴ | adj (2 ~A )⁻¹ |^8 aligned aligned & 2¹² 3³⁶ |(2 ~A )⁻¹ |¹⁶ & 2¹² 3³⁶ 1 |2 ~A |¹⁶ & 2¹² 3³⁶ 1 2⁴⁸| ~A |¹⁶ & 2¹² 3³⁶ 1 2⁴⁸ 3¹⁶ & 3²⁰ 2³⁶ =2⁻³⁶ 3²⁰ & ~m =-36 n =20 & ~m +2 n =4 aligned