If A and B are matrices of same order, then $(AB^T - BA^T)$ is always
Answer & explanation
Correct answer: option 2
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.