Let A and B be two square matrices of order 3 such that |A|=3 and |B|=2 . Then | A ^ T A ( adj (2 ~A ))⁻¹( adj (4 ~B ))( adj ( AB ))⁻¹ AA ^ T | is equal to :

Step-by-step solution

aligned & | A |=3,| ~B |=2 & | ~A ^ T A ( adj (2 ~A ))⁻¹( adj (4 ~B ))( adj ( AB ))⁻¹ AA ^ T | aligned ( array ccc =3 3 ( adj (2 ~A )⁻¹| | adj (4 ~B )| |( adj ( AB ))⁻¹ 3 3 . 1 | adj (2 ~A )| 2¹² 2^2 1 | adj ( AB )| array ) aligned & = 1 2^6| adj A | = 1 | adj B adj A | & = 1 2^6 3^2 = 1 2^2 3^2 & =3^4 1 2^6 3^2 2¹² 2^2 1 2^2 3^2 =64 & aligned