**What is a Symmetric Matrix?**

A **square Matrix A** is said to be **symmetric** if **for all i and j, where is an element present at position ( row and column in ****matrix A**) and is an element present at position ( row and column in **matrix A**).

In other words, we can say that **matrix A** is said to be **symmetric** if **transpose** of **matrix A** is equal to **matrix A** itself ().

Lets take an example of **matrix**

It is **symmetric matrix** because for all i and j

Example, , and

In other words, **transpose** of **Matrix A** is equal to **matrix A** itself () which means **matrix A** is **symmetric**.

Lets take another example of **matrix **

It is not **symmetric** because because =4 and =2.

In other words, we can say that **transpose** of **Matrix B** is not equal to **matrix B **().

**What is a Skew-Symmetric Matrix?**

**Square Matrix A **is said to be **skew-symmetric** if for all i and j. In other words, we can say that **matrix A** is said to be **skew-symmetric** if **transpose** of **matrix** **A **is equal to **negative** of **Matrix A **i.e ().

Note that all the **main diagonal elements** in **skew-symmetric** matrix are zero.

Lets take an example of **matrix** .

It is **skew-symmetric matrix** because for all i and j. Example, = -5 and =5 which means . Similarly, this condition holds true for all other values of i and j.

We can also verify that** Transpose** of **Matrix A** is equal to negative of **matrix A i.e .**

and .

We can clearly see that which makes **A skew-symmetric matrix**.

Lets take another example of **matrix .**

**Matrix B** is not **skew-symmetric** because or .

Note that in **skew-symmetric matrices**, to make , , ... All the main diagonal elements have to be zero.