b is the least square estimator of the general linear model $Y=X{\beta}$ where X is a n x p design matrix and $ Y\in R^p, {\beta}\in R^n$.
I want to prove blue part below. I worked some as you can find in the image I attached. But I found $Var(Xb-X{\beta})$ part is wrong since X doesn't have inverse.
Is there any other way I can show $Var(Xb-X{\beta})={\sigma}^2 I$? If I cannot is there any other way to prove this problem?
