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

$l=2, m = 3$

The correct answer is Option (3) → $l=2, m = 3$

Given: A is a skew-symmetric matrix.

Property: A matrix $A$ is skew-symmetric if $A^T = -A$

Let:

$A = \begin{bmatrix} 0 & l & -3 \\ -2 & 0 & 1 \\ m & -1 & 0 \end{bmatrix}$

Then:

$A^T = \begin{bmatrix} 0 & -2 & m \\ l & 0 & -1 \\ -3 & 1 & 0 \end{bmatrix}$

Now, set $A^T = -A$:

$\begin{bmatrix} 0 & -2 & m \\ l & 0 & -1 \\ -3 & 1 & 0 \end{bmatrix} = - \begin{bmatrix} 0 & l & -3 \\ -2 & 0 & 1 \\ m & -1 & 0 \end{bmatrix}$

⇒ Compare elements:

$-2 = -l \Rightarrow l = 2$

$m = -(-3) \Rightarrow m = 3$

Final Answer: l = 2 and m = 3