Which of the following is a skew-symmetric matrix?

\begin{bmatrix}0 & 2 & -3 \\ 2 & 0 & 5 \\ -3 & 5 & 0\end{bmatrix}

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\begin{bmatrix}1 & 2 \\ -2 & 1\end{bmatrix}

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\begin{bmatrix}0 & 2 & -3 \\ -2 & 0 & 5 \\ 3 & -5 & 0\end{bmatrix}

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\begin{bmatrix}0 & 2 & 3 \\ -2 & 0 & -5 \\ 3 & 5 & 0\end{bmatrix}

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CorrectNot quiteAnswer C

Correct answer: C

A skew-symmetric matrix has $a_{ji} = -a_{ij}$ : each element is the negative of its mirror image, and the diagonal is 0.
Only $\begin{bmatrix}0 & 2 & -3 \\ -2 & 0 & 5 \\ 3 & -5 & 0\end{bmatrix}$ passes on every pair.

Worth noting

$\begin{bmatrix} 1 & 2 \\ -2 & 1 \end{bmatrix}$ has the right signs off the diagonal, but a skew-symmetric matrix needs 0 on the diagonal.

Ten questions from Matrices, at your own pace.

Explanation