Suppose that an object with two indices has the property that $\displaystyle A(\mu,\nu)C^{\mu\nu}$ is a scalar for any arbitrary tensor $\displaystyle C^{\mu\nu}$. Show that $\displaystyle A(\mu,\nu)$ is a tensor.

Hint: start with the relationship $\displaystyle A^{'\nu}_{\mu}x^{'\mu}x^{'\nu}=A^\beta_\alpha x^\alpha x^\beta$