If A and B are matrices of same order, then $(AB^T - BA^T)$ is always

a skew symmetric matrix

The correct answer is Option (2) → a skew symmetric matrix

Given expression $AB^T-BA^T$

Take transpose

$(AB^T-BA^T)^T=(AB^T)^T-(BA^T)^T$

$=BA^T-AB^T$

$=-(AB^T-BA^T)$

Hence $(AB^T-BA^T)^T=-(AB^T-BA^T)$

This shows the matrix is skew-symmetric

The given expression is always a skew-symmetric matrix.