If $A$ and $B$ are symmetric matrices of same order, then $AB$ is symmetric if and only if

Matrices of any order can be added.

Matrix multiplication is commutative.

If $A$ and $B$ are two matrices of the same order, then$A-B=B-A$.

If $A$ and $B$ are two square matrices of the same order, then $AB=BA$.

If $A$ and $B$ are any two matrices of the same order, then $(AB{)}^{\text{'}}=A^{\text{'}}{B}^{\text{'}}$.

If $(AB{)}^{\text{'}}=B^{\text{'}}{A}^{\text{'}},$ where $A$ and $B$ are not square matrices, then number of rows in $A$ is equal to number of columns in $B$ and number of columns in $A$ is equal to number of rows in $B$.