The inverse of a skew symmetric matrix of odd order is

On using elementary column operations $C_2\to C_2-2C_1$ in the following matrix equation $\left[\begin{array}{cc}1& -3\\ 2& 4\end{array}\right]=\left[\begin{array}{cc}1& -1\\ 0& 1\end{array}\right]\left[\begin{array}{cc}3& 1\\ 2& 4\end{array}\right]$ , we have

On using elementary row operation $R_1\to R_1-3R_2$ in the following matrix equation $\left[\begin{array}{ll}4& 2\\ 3& 3\end{array}\right]=\left[\begin{array}{ll}1& 2\\ 0& 3\end{array}\right]\left[\begin{array}{ll}2& 0\\ 1& 1\end{array}\right]$, we have