Symmetric Matrix

A Square Matrix is a Symmetric Matrix if it is equal to its Transpose, $A = A^T$ .

If a matrix is a Symmetric Matrix, then the following is true for all its elements:

$a_{ij}=a_{ji}$

An example of a Symmetric Matrix is shown below:

$\begin{bmatrix} 1 & 5 & 6 & 7 \\ 5 & 2 & 8 & 9 \\ 6 & 8 & 3 & 10\\ 7 & 9 & 10 & 4 \end{bmatrix}$

If A and B are symmetric matrices then the matrix multiplication of A and B is commutative, AB=BA.