Question 1199095
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                Let solve it step by step.



<pre>
(1)  First calculate determinant of the given matrix {{{A^(-1)}}}.

     Use the basic definition of the determinant in an expanded form.

     You will get  {{{det(A^(-1))}}} = {{{1/3}}}.




(2)  It implies, due to well known properties of determinants, that

        det(A) = {{{(1/3)^(-1)}}} = 3.



(3)  Finally, use another well known formula of linear algebra, which for 3x3 matrix A takes the form

        det(Adj(A)) = {{{(det(A))^2}}}.


     We just know from  (2)  that det(A) = 3.  Therefore,

        det(Adj(A)) = {{{3^2}}} = 9.


<U>ANSWER</U>.  det(Adj(A)) = 9.
</pre>

Solved, with all necessary explanations.