Given information:
A is a 3 x 3 matrix, whose (i, j)-th element, ai,j = (i-j)3.

To determine whether the matrix A is symmetric, skew-symmetric, unitary, or null, we need to understand the properties of these types of matrices.

Symmetric Matrix:
A matrix is said to be symmetric if it is equal to its transpose. In other words, if A = A^T, then A is a symmetric matrix.

Skew-symmetric Matrix:
A matrix is said to be skew-symmetric if it is equal to the negative of its transpose. In other words, if A = -A^T, then A is a skew-symmetric matrix.

Unitary Matrix:
A matrix is said to be unitary if its conjugate transpose is equal to its inverse. In other words, if A*A^H = A^H*A = I, where A^H is the conjugate transpose of A, then A is a unitary matrix.

Null Matrix:
A matrix is said to be null if all its elements are zero.

Now, let's determine the properties of matrix A based on the given information.

Properties of matrix A:
a11 = (1-1)^3 = 0
a12 = (1-2)^3 = -1
a13 = (1-3)^3 = -8
a21 = (2-1)^3 = 1
a22 = (2-2)^3 = 0
a23 = (2-3)^3 = -1
a31 = (3-1)^3 = 8
a32 = (3-2)^3 = 1
a33 = (3-3)^3 = 0

Transpose of A:
A^T = [0 -1 -8; 1 0 -1; 8 1 0]

Negative of transpose of A:
-A^T = [0 1 8; -1 0 1; -8 -1 0]

Based on the above calculations, we can conclude that:

- A is not a symmetric matrix, since A is not equal to its transpose.
- A is a skew-symmetric matrix, since A is equal to the negative of its transpose.
- A is not a unitary matrix, since A is not a square matrix.
- A is not a null matrix, since it has non-zero elements.

Therefore, the correct answer is option B, i.e., A is a skew-symmetric matrix.