Group Theory - Question on normal subgroup

This is from Herstein, q#6, section 2.9 pg 75

Question - order(G) = p^2, where p is a prime. Prove any normal subgroup, N, of order p, must lie in the center of G.

I have been trying this for a while, but stuck. This question comes much before concepts like class equation of G, Sylow's theorm etc. So argument used should be more basic. Any help/pointers to get me started plz?

I was trying to use the fact that N is cyclic and normal but was not successful.