If $p$ is an odd prime and $\gcd(ab, p) = 1$, prove that at least one of $a, b$, or $ab$ is a quadratic residue of p.

Question

Anyone can check my proof ? Consider $x^{2}\equiv ab \pmod p$ If it is congruence $\gcd (x^{2},p)$ must equal. Since $\gcd(a b,p) = 1$ it follow $\gcd(x^{2},p)=\gcd(a,p)=\gcd(b,p)=1$ therefore it make the quardratric residues can be $a,b,ab$