# product of coefficients of regressions x to y and y to x

I was asked that if $$y\sim N(0,a^2)$$ and $$x\sim N(0,b^2),$$ what is the product of coefficients of the regression x to y and the regression y to x.

I think this is a very popular question for OLS (product is R-squared). But here it is like EIV. To be honest, I even do not know how to build the linear relation between x and y, since EIV builds the linear between their means. But here their means are zero identically.