1. The problem statement, all variables and given/known data Let A be an invertible 3x3 matrix. Suppose it is known that: A = [u v w 3 3 -2 x y z] and that adj(A) = [a 3 b -1 1 2 c -2 d] Find det(A) (answer without any unknown variables) 2. Relevant equations 3. The attempt at a solution I found A^(-1) to be equal to (1/det(A)) * adj(A) So, then re-arranging the formula; I*det(A) = A*adj(A) So then det(A) = [u v w 3 3 -2 x y z] * [a 3 b -1 1 2 c -2 d] I know the solution to this problem is det(A) = 16. Therefore it must be that [3 3 -2] * [3 1 2] = det(A) But, what I am confused about is: Why is the det equal only to the position (2,2) of the matrix A*adj(A)? As the solution is taken as the position a_(2,2)... Thanks!