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Let A be a non singular matrix of order 3 then det(adjA) is ?

adjA=A.A-1 let the order of the matrix A is n.
adjA=AA-1=AnA-1=AnA-1=An-1
if the order of the matrix A is 3.
det(adjA)=A3-1=A2

hope this helps you
 

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adj(A) = |A| . I

where I is identity matrix

|adj(A)| = ||A| . I |

|adj(A)| = |A|n-1 . | I|

where n is thre order of matrix A

which is given 3

|adj(A)| = |A|2

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