**3.5.1 Symmetric matrix:** A square matrix A = [aij] is said to be symmetric if its (i, j)^{th} element is the same as its (j, i)^{th} element.

i.e. A = A^{T}

A = A^{T}

Therefore, A is symmetric matrix.

**3.5.2 Skew symmetric matrix:** A square matrix A = [a**ij**] is said to be skew-symmetric if the (i, j)^{th} element of A is the negative of the (j, i)^{th} element of A

i.e. A ^{T} = -A

Therefore, A^{T} = -A

**Properties of Symmetric and skew-symmetric matrix**

- i) A square matrix A is said to be skew-symmetric if A' = -A.
- ii) The diagonal elements of a skew-symmetric matrix are all zero.

**Examples**:

That is any square matrix can be expressed as the sum of a symmetric matrix and a skew-symmetric matrix.

v) A matrix which is both symmetric and skew symmetric is a zero matrix.**To Schedule a Symmetric And Skew-Symmetric Matrix tutoring session click here
To submit Symmetric And Skew-Symmetric Matrix assignment click here.**

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