How to prove the following property of the matrices?

Question

If every element of a matrix $X$ is greater than zero and if $X=X^T$ then how can we show that $X$ is a positive definite matrix?

Answer 1

We can't, because it's false. For instance, consider $\begin{pmatrix}a&b\\ b&d\end{pmatrix}$ with $a,d$ small and $b$ large.