The difference of two different skew-symmetric matrices is:

The correct answer is Option (4) → Skew-symmetric matrix

Let \(A\) and \(B\) be skew-symmetric matrices:

\(A^T = -A\) and \(B^T = -B\)

Consider the difference \(C = A - B\).

Transpose of \(C\):

\[ C^T = (A - B)^T = A^T - B^T = -A - (-B) = -A + B = -(A - B) = -C \]

Since \(C^T = -C\), \(C\) is skew-symmetric.

Therefore, the difference of two skew-symmetric matrices is a skew-symmetric matrix.