Understanding last step of OLS estimator variance proof

Question

I am missing something about the last step of the variance of the OLS estimator for $b$. I understand up to the point when $\sigma^2$ is derived due to errors being mutually independent. However, when we go from this:

$V(b)=\sigma²(X'X)^{-1}X'X(X'X)^{-1}$

to

$V(b)=\sigma²(X'X)^{-1}$

Could you help me figuring out which properties of $X$ or any matrix whatsoever, make that substitution possible?

Answer 1

In this step you're simply canceling $(X'X)$ and $(X'X)^{-1}$ to get an identity matrix.