The correct answer is (A) - (IV), (B) - (III), (C) - (I), (D) - (II).

Let us analyze each term in List-I and match it with the correct description in List-II:

1. Matching (A): A^T = A
By definition, a square matrix $A$ is called a symmetric matrix if it is equal to its transpose, which is written as:
$$A^{\text{T}}=A$$
Therefore, (A) matches with (IV).

2. Matching (B): A^T = -A
By definition, a square matrix $A$ is called a skew-symmetric matrix if the transpose of the matrix is equal to the negative of the matrix itself, which is written as:
$$A^{\text{T}}=\&\#x2212;A$$
Therefore, (B) matches with (III).

3. Matching (C): |A| = 0
A square matrix $A$ is defined as a singular matrix if its determinant is equal to zero, which is represented by:
$$\left|A\right|=0$$
Therefore, (C) matches with (I).

4. Matching (D): |A| ≠ 0
A square matrix $A$ is defined as a non-singular matrix if its determinant is not equal to zero, which is represented by:
$$\left|A\right|\&\#x2260;0$$
Therefore, (D) matches with (II).

Combining all the individual matches, we get:
(A) → (IV), (B) → (III), (C) → (I), and (D) → (II).