Question

1. Show that the matrix A=$\begin{bmatrix}1&-1&5\\\\-1&2&1\\\5&1&3\end{bmatrix}$ is a symmetric matrix.
2. Show that the matrix A=$\begin{bmatrix}0&1&-1\\\\-1&0&1\\\1&-1&0\end{bmatrix}$ is a skew symmetric matrix

Answer 1

(i) We have: A'=$\begin{bmatrix}1&-1&5\\\\-1&2&1\\\5&1&3\end{bmatrix}$=A so A'=A

(i) We have: A'=$\begin{bmatrix}0&-1&1\\\1&0&-1\\\\-1&1&0\end{bmatrix}$=-$\begin{bmatrix}0&1&-1\\\\-1&0&1\\\1&-1&0\end{bmatrix}$=-A

so A'=A Hence, A is a skew-symmetric matrix.