(i) For a symmetric matrix aij = aji
Now,
![A=\left[ \begin{matrix} 1 & -1 & 5 \\ -1 & 2 & 1 \\ 5 & 1 & 3 \end{matrix} \right]](https://s0.wp.com/latex.php?latex=A%3D%5Cleft%5B+%5Cbegin%7Bmatrix%7D+1+%26+-1+%26+5+%5C%5C+-1+%26+2+%26+1+%5C%5C+5+%26+1+%26+3+%5Cend%7Bmatrix%7D+%5Cright%5D+&bg=ffffff&fg=000&s=2 "A=\left[ \begin{matrix} 1 & -1 & 5 \\ -1 & 2 & 1 \\ 5 & 1 & 3 \end{matrix} \right]")
(i) Show that the matrix $A=\left[\begin{array}{ccc}1 & -1 & 5 \\ -1 & 2 & 1 \\ 5 & 1 & 3\end{array}\right] $is a symmetric matrix.(ii) Show that the matrix $$ A=\left[\begin{array}{ccc} 0 & 1 & -1 \\ -1 & 0 & 1 \\ 1 & -1 & 0 $$is a skew-symmetric matrix.
(i) Show that the matrix $A=\left[\begin{array}{ccc}1 & -1 & 5 \\ -1 & 2 & 1 \\ 5 & 1 & 3\end{array}\right] $is a symmetric matrix.(ii) Show that the matrix $$ A=\left[\begin{array}{ccc} 0 & 1 & -1 \\ -1 & 0 & 1 \\ 1 & -1 & 0 $$is a skew-symmetric matrix.