Show that the matrix $A = \begin{bmatrix} 0 & 1 & -1 \\ -1 & 0 & 1 \\ 1 & -1 & 0 \end{bmatrix}$ is a skew-symmetric matrix.

(N/A) matrix $A$ is said to be skew-symmetric if $A^{\prime} = -A$.
Given $A = \begin{bmatrix} 0 & 1 & -1 \\ -1 & 0 & 1 \\ 1 & -1 & 0 \end{bmatrix}$.
The transpose of matrix $A$,denoted by $A^{\prime}$,is obtained by interchanging its rows and columns:
$A^{\prime} = \begin{bmatrix} 0 & -1 & 1 \\ 1 & 0 & -1 \\ -1 & 1 & 0 \end{bmatrix}$.
Now,factor out $-1$ from the matrix $A^{\prime}$:
$A^{\prime} = -1 \times \begin{bmatrix} 0 & 1 & -1 \\ -1 & 0 & 1 \\ 1 & -1 & 0 \end{bmatrix} = -A$.
Since $A^{\prime} = -A$,the matrix $A$ is a skew-symmetric matrix.