Question

If $A=\left(\begin{array}{cc}5& a\\ b& 0\end{array}\right)$ and A is symmetric matrix, show that a$=$b.

Answer 1

$A=\left(\begin{array}{cc}5& a\\ b& 0\end{array}\right)$

A is symmetric matrix $\to A=A^T$

$\Rightarrow \left(\begin{array}{cc}5& a\\ b& 0\end{array}\right)=\left(\begin{array}{cc}5& b\\ a& 0\end{array}\right)$

So to be symmetric $a=b$.

Hence proved.