Given that |adj‌A|=x and |adj‌B|=y, we are tasked with finding |(adj(AB))−1|. First, recognize that the determinant of the adjugate of a matrix can be expressed with respect to the determinants of the matrix itself. Using this relation, we have: |adj(AB)|=|adj(adj(A))|⋅|adj(adj(B))| The inverse of the adjugate adjoint product can be decomposed as: |(adj(AB))−1|=∣(adj‌B)−1(adj‌A)−1)∣ Because |adj‌A|=x and |adj‌B|=y, the properties of determinants give us: ‌|(adj‌A)−1|=‌
1
|adj‌A|
=‌
1
x
‌|(adj‌B)−1|=‌
1
|adj‌B|
=‌
1
y
Thus, the determinant of the inverse of the product is: |(adj(AB))−1|=‌