**Skew symmetric matrix** is a square matrix Q=[x_{ij}] in which (i, j)^{th} element is negative of the (j, i)^{th} element i.e. x_{ij} = -x_{ji} for all values of i and j. In other words, a square matrix (Q) which is equal to negative of its transpose is known as skew-symmetric matrix i.e. Q^{T} = -Q.

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## Skew symmetric matrix examples

The example of a skew-symmetric matrix of order 2 (or matrix size is 2 x 2) is given as

\[C=\begin{bmatrix} 0 &2 \\ -2& 0 \end{bmatrix}\]

The example of a skew-symmetric matrix of order 3 (or matrix size is 3 x 3) is given as

\[D=\begin{bmatrix} 0 &8 &2 \\ -8& 0 &5 \\ -2& -5 & 0 \end{bmatrix}\]

## Skew symmetric matrix properties

1. All the diagonal elements in a skew-symmetric matrix are always zero.

2. If P be a skew-symmetric matrix then P^{T} = -P.

**Let B be any matrix then**

1. $\frac{B-B^T}{2}$is always a skew-symmetric matrix.