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

Toolbox:
• A square matrix A=[a$_{ij}$] is said to be skew symmetric if A'=-A that is $[a_{ij}]= -[a_{ji}]$ for all possible value of i and j.
• In a skew symmetric matrix all elements along the principal diagonal are zero.
Step1:
Given:
A = $\begin{bmatrix} 0 & 1 & -1 \\ -1 & 0 & 1 \\ 1 & -1 & 0 \end{bmatrix}$
We know that A'=-A.
$\Rightarrow a_{ij}=-a_{ij}$
Step2:
Put i=j,we have
$a_{ii}=-a_{ii}$
$\Rightarrow 2a_{ii}=0$
$a_{ii}=0.$
Hence the diagonal elements of a given matrix are zero.
$\Rightarrow$ matrix A-Skew symmetric matrix.