Given : $A=\left[\begin{array}{ccc}2 & 0 & -3 \\ 4 & 3 & 1 \\ -5 & 7 & 2\end{array}\right]$
Since, each and every matrix can be written as sum of symmetric \& skew symmetric matrix.
$\therefore$ A can be written as sum symmetric matrix $P$ and skew symmetric matrix Q.
where $\mathrm{P}=\frac{1}{2}\left[\mathrm{~A}+\mathrm{A}^{\mathrm{T}}\right]$
$$
\mathrm{Q}=\frac{1}{2}\left[\mathrm{~A}-\mathrm{A}^{\mathrm{T}}\right]
$$
$$
\begin{aligned}
& \text { Now, } A^T=\left[\begin{array}{ccc}
2 & 4 & -5 \\
0 & 3 & 7 \\
-3 & 1 & 2
\end{array}\right] \\
& \therefore P=\frac{1}{2}\left[\begin{array}{ccc}
4 & 4 & -8 \\
4 & 6 & 8 \\
-8 & 8 & 4
\end{array}\right]=\left[\begin{array}{ccc}
2 & 2 & -4 \\
2 & 3 & 4 \\
-4 & 4 & 2
\end{array}\right] \\
& Q=\frac{1}{2}\left[\begin{array}{ccc}
0 & -4 & 2 \\
4 & 0 & -6 \\
-2 & 6 & 0
\end{array}\right]=\left[\begin{array}{ccc}
0 & -2 & 1 \\
2 & 0 & -3 \\
-1 & 3 & 0
\end{array}\right] \\
& \mathrm{P}^T=\left[\begin{array}{ccc}
2 & 2 & -4 \\
2 & 3 & 4 \\
-4 & 4 & 2
\end{array}\right] Q^T=\left[\begin{array}{ccc}
0 & 2 & -1 \\
-2 & 0 & +3 \\
1 & -3 & 0
\end{array}\right]
\end{aligned}
$$
$\mathrm{P}^{\mathrm{T}}-\mathrm{Q}^{\mathrm{T}}=\left[\begin{array}{ccc}2-0 & 2-2 & -4+1 \\ 2+2 & 3-0 & 4-3 \\ -4-1 & 4+3 & 2-0\end{array}\right]=\left[\begin{array}{ccc}2 & 0 & -3 \\ 4 & 3 & 1 \\ -5 & 7 & 2\end{array}\right]$