Question 1042632
We have the fundamental relation

{{{A*adj(A) = abs(A)I[3]}}}, 

where {{{abs(A)}}} is the determinant of A.

===> {{{abs(A)*(adj(A)) = abs(A)^3}}},

since A is of order 3.  (The determinant was applied on both sides.)

===>{{{adj(A) =  abs(A)^2}}},

===> {{{abs(A)^2 = 36}}} ===> |A| = 6 or |A| = -6.

===>  {{{abs(A^T) = 6}}} or  {{{abs(A^T) = -6}}}, since {{{abs(A) = abs(A^T)}}}.