If \( A \) and \( B \) are matrices of the same order, then \( AB^{T}-BA^{T} \) is a
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Skew-symmetric matrix
A matrix M is skew-symmetric when \( M^{T}=-M \). Using \( (XY)^{T}=Y^{T}X^{T} \) and \( (B^{T})^{T}=B \),
\( (AB^{T})^{T}=BA^{T} \)
\( (BA^{T})^{T}=AB^{T} \)
So
\( (AB^{T}-BA^{T})^{T}=BA^{T}-AB^{T} \)
\( =-(AB^{T}-BA^{T}) \)
So \( AB^{T}-BA^{T} \) is a skew-symmetric matrix.