If A and B are symmetric matrices, then write the condition for which AB is also symmetric.

Given: AB is symmetric.

$\Rightarrow(A B)^{T}=A B$

$\Rightarrow B^{T} A^{T}=A B \quad\left[\because(A B)^{T}=B^{T} A^{T}\right]$

$\Rightarrow B A=A B \quad\left[\because A\right.$ and $B$ are symmetric matrices, so $A^{T}=A$ and $\left.B^{T}=B\right]$

Thus, $A B$ is also symmetric, if $A B=B A$.