please solve If A 3 A epsilon R then what are the values A1

   please solve

If |A| = 3, A epsilon R, then what are the values |A^-1|, |adj(A)| and |adj (A^-1)|?

Solution

Given that |A| = 3

1) |A^-1| = 1/ |A| = 1/3

2) |adj(A)| = |A|^n-1 where n is order of the square matrix

= 3^n-1

3) |adj(A^-1)| = 1/ |A|^n-1  where n is order of the square matrix

= 1/3^n-1