# are all elements of ZpxZp in ECC definite over Zp

are all elements of ZpxZp in ECC (elliptic curve) definite over Zp ?

otherwise: assume G a base point of ECC and n the order of G.

why n is equal or nother to p*p ? (p a prime number).

(Think to a Bitcoin Curve: y^2 = x^3 + 7).

All points have two coordinates. Both coordinates lies in $\mathbb{Z}_p$ (I'm assuming a curve defined over $GF(p)$).
But not all elements of $\mathbb{Z}_p \times \mathbb{Z}_p$ are valid points for an elliptic curve. Only those which verifies the curve's equation.
So if you select all elements of $\mathbb{Z}_p \times \mathbb{Z}_p$ and call the first $x$ and the second $y$, and when you put them in (for example) $y^2 = x^3 + 7$ if you obtain an equality, then your $x$ and $y$ form a valid point belonging to your curve.
If you count them (and add the point at infinity, which is a special point who can't be represented as $(x,y)$), their number will be the cardinality of the curve, which is a number related to your $p$ through Hasse's theorem but can be smaller or bigger.