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(B) matrix $A$ is skew-symmetric if $A^T = -A$. For a skew-symmetric matrix,the diagonal elements must be zero,so $a = 0$. Also,the condition $A_{ij}

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$1$

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(B) matrix $A$ is skew-symmetric if $A^T = -A$. For a skew-symmetric matrix,the diagonal elements must be zero,so $a = 0$. Also,the condition $A_{ij} = -A_{ji}$ must hold for all $i, j$. Comparing the elements: $A_{12} = 2$ and $A_{21} = b$,so $b = -2$. $A_{13} = -3$ and $A_{31} = c$,so $c = -(-3) = 3$. $A_{23} = 4$ and $A_{32} = -4$,which satisfies $4 = -(-4)$. Thus,$a = 0$,$b = -2$,and $c = 3$. Calculating the sum: $a+b+c = 0 + (-2) + 3 = 1$.

If the matrix $\begin{bmatrix} a & 2 & -3 \\ b & 0 & 4 \\ c & -4 & 0 \end{bmatrix}$ is a skew-symmetric matrix,then $a+b+c=$

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