Let A and B be square matrices of order 3, then det $[(A - A^T) + (B - B^T)]$ is equal to
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0
Given:
$A$ and $B$ are square matrices of order 3
Expression: $\det[(A - A^T) + (B - B^T)]$
Observation: $(A - A^T)$ and $(B - B^T)$ are skew-symmetric matrices
Property: Determinant of any odd-order skew-symmetric matrix = 0
Sum of skew-symmetric matrices is also skew-symmetric
Since order = 3 (odd), determinant = 0