If A is a square matrix of order 5 and 9 ~A ⁻¹=4 ~A ^ T find the number of digits in adj ( adj ( adj A )) ( where A , A ^ and adj ( A ) denotes the inverse, transpose and adjoint of matrix A respectively) ( 3=0.477, 2=0.303)

Step-by-step solution

9 ~A ⁻¹=4 ~A ^T |9 ~A ⁻¹ |= |4 ~A ^ T | 9^5 1 | ~A | =4^5| ~A | | A |= ( 3 2 )^5| adj adj adj A |=| A |^ 4^3 = ( 3 2 )³²⁰ No. of digits in | adj adj adj A |= [ ( 3 2 )³²⁰ ]+1=56 . (Where [.] denotes greatest integer function).