(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 $A=\left[\begin{array}{ccc}0 & 1 & -1 \\ -1 & 0 & 1 \\ 1 & -1 & 0\end{array}\right]$ is a skew symmetric matrix
(i) We have:
$A^{\prime}=\left[\begin{array}{ccc}1 & -1 & 5 \\ -1 & 2 & 1 \\ 5 & 1 & 3\end{array}\right]=A$
$\therefore A^{\prime}=A$
Hence, $A$ is a symmetric matrix
(ii) We have:
$A^{\prime}=\left[\begin{array}{ccc}0 & -1 & 1 \\ 1 & 0 & -1 \\ -1 & 1 & 0\end{array}\right]=-\left[\begin{array}{ccc}0 & 1 & -1 \\ -1 & 0 & 1 \\ 1 & -1 & 0\end{array}\right]=-A$
$\therefore A^{\prime}=-A$
Hence, $A$ is a skew-symmetric matrix.
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.