Lebesgue measurable sets: $1 \in A-A$

Question

Let $A \subset [-1, 1]$ Lebesgue measurable with $\lambda (A) > 1$. Why does it hold true that $1 \in A-A$, where $ A -A =$ {$x-y: x, y \in A$} ?

Answer 1

Consider $A\cap[0,1]-1$ and $A\cap[-1,0]$. By $\lambda(A)>1$, they must have non-empty intersection.