If \(A\) and \(B\) are symmetric matrices of the same order, then which one of the following is not true?

Given, \(A\) and \(B\) are symmetric matrix of same order.
\[
\Rightarrow \quad A=A^{\prime}, B=B^{\prime}
\]
(i) \((A+B)^{\prime}=A^{\prime}+B^{\prime}=A+B \quad\) [from Eq. (i)] \(\Rightarrow(A+B)\) is symmetric.
(ii) \((A-B)^{\prime}-\Lambda^{\prime}-B^{\prime}-\Lambda-B\) [from Eq. (i)] \(\Rightarrow(A-B)\) is symmetric.
\[
\text { (iii) } \begin{aligned}
(A B+B A)^{\prime} &=(A B)^{\prime}+(B A)^{\prime} \\
&=B^{\prime} A^{\prime}+A^{\prime} B^{\prime} \\
&=B A+A B \quad\lfloor\text { from Eq. (i) }] \\
&=(A B+B A)
\end{aligned}
\]
\(\Rightarrow(A B+B A)\) is symmetric.
\[
\text { (iv) } \begin{aligned}
(A B-B A)^{\prime} &=(A B)^{\prime}-(B A)^{\prime} \\
&=B^{\prime} A^{\prime}-A^{\prime} B^{\prime} \\
&=B A-A B \quad \text { [from Eq. (i)] } \\
&=-(A B-B A)
\end{aligned}
\]
\(\Rightarrow(A B-B A)\) is skew-symmetric matrix.