Question: Prove that the product of two odd functions is an even function.

I know a few basic facts about even and odd functions:

In an even function, e(x)=e(-x)

In an odd function, o(-x)=-o(x)

An even function is a reflection across the y-axis.

An odd function is a reflection across the origin.

where e and o are even and odd functions respectively.

How would I go about using this knowledge, and possibly other information, to complete this proof? Any suggestions are appreciated.