Question

Matrix $A=\left[\begin{array}{ccc}0& 2b& -2\\ 3& 1& 3\\ 3a& 3& -1\end{array}\right]$ is given to be symmetric, find values of $a$ and $b$

Answer 1

$A=\left|\begin{array}{ccc}0& 2b& -2\\ 3& 1& 3\\ 3a& 3& -1\end{array}\right|$

Since the matrix is symmetric, the off diagonal elements need to be symmetrical about the diagonal.

So, $a_{12}=a_{21},a_{13}=a_{31}$

$\Rightarrow 2b=3$

$\Rightarrow b=\frac{3}{2}$

Also, $3a=-2$

$\Rightarrow a=\frac{-2}{3}$