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(D) Given that $A$ and $B$ are symmetric matrices of the same order,we have $A^T = A$ and $B^T = B$. $(i)$ $(A+B)^T = A^T + B^T = A+B$. Thus,$A+B$ is

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$AB-BA$ is symmetric

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(D) Given that $A$ and $B$ are symmetric matrices of the same order,we have $A^T = A$ and $B^T = B$. $(i)$ $(A+B)^T = A^T + B^T = A+B$. Thus,$A+B$ is symmetric. (ii) $(A-B)^T = A^T - B^T = A-B$. Thus,$A-B$ is symmetric. (iii) $(AB+BA)^T = (AB)^T + (BA)^T = B^T A^T + A^T B^T = BA + AB = AB+BA$. Thus,$AB+BA$ is symmetric. (iv) $(AB-BA)^T = (AB)^T - (BA)^T = B^T A^T - A^T B^T = BA - AB = -(AB-BA)$. Thus,$AB-BA$ is skew-symmetric,not symmetric. Therefore,the statement '$AB-BA$ is symmetric' is not true.

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

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