## Elementary Linear Algebra 7th Edition

$A$ is symmetric.
Let the matrix $A$ be given by $$A=\left[\begin{array}{ccc}{2} &{1} \\{1}& {3} \end{array}\right].$$ Since Since $a_{ij}=a_{ji}$ for all $i,j$, then $A$ is symmetric. Also, this can be shown by the fact that $$A^T=\left[\begin{array}{ccc}{2} &{1} \\{1}& {3} \end{array}\right] =A.$$