If \( A=\begin{bmatrix}0 & a & -3\\2 & 0 & -1\\b & 1 & 0\end{bmatrix} \) is a skew-symmetric matrix, then
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( a=-2,b=3 \)
A matrix is skew-symmetric when \( A^T=-A \), that is, \( a_{ji}=-a_{ij} \) for every i, j.
\( \displaystyle a_{12}=-a_{21}:\ a=-2 \)
\( \displaystyle a_{31}=-a_{13}:\ b=-(-3)=3 \)
The remaining pair agrees: \( a_{23}=-1 \) and \( a_{32}=1 \), and all diagonal entries are 0.
Why the other options are incorrect
Option (1) \( a=2,b=3 \) — Incorrect. With a = 2, \( a_{12}=a_{21} \); that is the condition for a symmetric matrix, not a skew-symmetric one.
Option (3) \( a=-2,b=-3 \) — Incorrect. b = −3 gives \( a_{31}=a_{13} \), again the symmetric condition.
Option (4) \( a=2,b=-3 \) — Incorrect. Both values copy the entries opposite them, \( a_{12}=a_{21} \) and \( a_{31}=a_{13} \), which makes those pairs symmetric.