If $f(ta,tb) = f(a,b)$ $\forall t \neq 0$, then can we conclude that $f$ is a homogeneous polynomial of degree 1?
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Homogeneous of degree $1$ would be $f(ta,tb) = t^1f(a,b)$. In your case you have that $f(ta,tb) = f(a,b)=t^0f(a,b)$. This would mean homogeneous of degree $0$.
Here are some nice lecture notes and finer details on "functions homogeneous of degree $0$".