Prove that a unit matrix is its own inverse. Is the converse true?

Express as a sum of a symmetric and a skew symmetric matrix

$\left[\begin{array}{ccc}1& 2& 3\\ 4& 0& 1\\ -1& 5& -2\end{array}\right]$

Express as a sum of a symmetric and a skew symmetric matrix

$\left(\begin{array}{ccc}2& -1& 3\\ 5& 7& -2\\ 1& 4& 6\end{array}\right)$

Express as a sum of a symmetric and a skew symmetric matrix

$\left(\begin{array}{l}x\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}a\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}b\\ a\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}y\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}c\\ b\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}c\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}z\end{array}\right)$

Express as a sum of a symmetric and a skew symmetric matrix

$\left(\begin{array}{cc}0& x\\ -x& 0\end{array}\right)$

Express as a sum of a symmetric and a skew symmetric matrix

$\left(\begin{array}{cc}1& 5\\ 7& -3\end{array}\right)$

Express as a sum of a symmetric and a skew symmetric matrix

$\left(\begin{array}{cc}4& -3\\ 1& 2\end{array}\right)$