Algebra

Matrices & Determinants

Easy

core

If $A = \begin{bmatrix}0 & a & -3 \\ 2 & 0 & -1 \\ b & 1 & 0\end{bmatrix}$ is a skew-symmetric matrix, then

$a=2, b=3$

$a=-2, b=3$

$a=-2, b=-3$

$a=2, b=-3$

✅ Correct Option: 2

Skew-symmetry requires $a_{ij}=-a_{ji}$ .

From $a_{12}=-a_{21}$ : $a=-2$ .

From $a_{13}=-a_{31}$ : $-3=-b$ , so $b=3$ .

The pair $a_{23}=-1$ , $a_{32}=1$ is already consistent.

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If A=[0a−320−1b10]A = \begin{bmatrix}0 & a & -3 \\ 2 & 0 & -1 \\ b & 1 & 0\end{bmatrix}A=​02b​a01​−3−10​​ is a skew-symmetric matrix, then