If A and B are two skew-symmetric matrices of same order,

It is given that, $A$ and $B$ are two skew-symmetric matrices of same order.

$\therefore A^{T}=-A$ and $B^{T}=-B$           ....(1)

Now, the matrix $A B$ is symmetric if

$(A B)^{T}=A B$          (A matrix $X$ is symmetric if $X^{T}=X$ )

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

$\Rightarrow(-B)(-A)=A B \quad[$ Using (1) $]$

$\Rightarrow B A=A B$

Thus, if $A$ and $B$ are two skew-symmetric matrices of same order, then $A B$ is symmetric if $A B=B A$.

If $A$ and $B$ are two skew-symmetric matrices of same order, then $A B$ is symmetric if $A B=B A$