The question I want to answer is:
Show that $A_{5}$ is generated by $3$-cycles.
And I got a hint that: it suffices to show that every product $(a b)(c d)$ of two transpositions is a product of $3$-cycles.
But I do not understand how the hint will prove the required, could anyone explain that for me please?
EDIT: I am not asking about the proof, I am asking about why proving the hint proves the required.