For an invertible matrix $A$, the fundamental relationship $A \cdot \text{adj}(A) = \det(A) \cdot I$ holds, where $\text{adj}(A)$ is the adjugate (classical adjoint) matrix. If $\det(A) = 4$ and the $(2,1)$-entry of $\text{adj}(A)$ is 8, what is the $(2,1)$-entry of $A^{-1}$?