Question about definite positive symmetric bilinear form

Question

Let $A$ be the matrix of a positive definite symmetric bilinear form. Prove $a_{11}a_{nn}\ge a_{1n}a_{n1}$.

I don't really have a clue of how to solve this.

Answer 1

Hint: if $A$ is positive definite, the $2\times2$ principal submatrix $\pmatrix{a_{11}&a_{1n}\\ a_{n1}&a_{nn}}$ is also positive definite.