The given information is as follows:
- The eigenvalues of a non-singular matrix A are 3 and -2.
- The determinant of matrix A, |A|, is 4.


To find the sum of the eigenvalues of the adjoint matrix of A (adj(A)), we need to calculate the eigenvalues of adj(A).

Step 1: Recall that for any matrix A, the determinant of the adjoint matrix adj(A) is equal to the determinant of A raised to the power of (n-1), where n is the size of the matrix. In this case, since |A| = 4, we have |adj(A)| = 4^(n-1).

Step 2: The determinant of adj(A) is also equal to the product of its eigenvalues. Therefore, we can write |adj(A)| = λ1 * λ2 * ... * λn, where λ1, λ2, ..., λn are the eigenvalues of adj(A).

Step 3: From Step 1, we know that |adj(A)| = 4^(n-1). We can also write the product of the eigenvalues as λ1 * λ2 * ... * λn = 4^(n-1).

Step 4: Since we are given that the eigenvalues of A are 3 and -2, we have (λ1 * λ2 * ... * λn) = 3 * -2 = -6.

Step 5: Comparing the equations from Step 3 and Step 4, we have -6 = 4^(n-1).

Step 6: Solve for n-1: n-1 = log4(-6).

Step 7: Since the logarithm of a negative number is undefined, we can conclude that there is no solution for n-1. This implies that there is no adjoint matrix for A, as the size of the matrix is undefined.


Based on the given information, it is not possible to calculate the sum of the eigenvalues of adj(A) because the adjoint matrix does not exist. Therefore, the answer to this question cannot be determined.