So, I'm new to linear regression and this question might be easy, but I didn't find a similar question (one with the same regression model) on the internet.
Suppose that $X_1$ and $X_2$ are two independent predictors, and that we fit the linear regression model $$E(X_1X_2|X_1,X_2)=a_0+a_1X_1+a_2X _2$$ using ordinary least squares (OLS). I want to show that the OLS estimators converge to $a_0=-E(X_1)E(X_2)$, $a_1=E(X_2)$ and $a_2=E(X_1)$.
I really don't know how to start. I know I probably have to use this matrix $$ \begin{bmatrix} X_{1}^2 & X_{1}X_{2} \\ X_{2}X_{1} & X_{2}^2 \end{bmatrix} $$ but I don't even know wich formula I have to use in this case in order to find the OLS estimators. Thank you in advance!