# How to prove that $X^T$e = 0

I need to prove that $X^T e$ = 0 where $e$ is the residual in multiple linear regression model in matrix algebra?

I need some guidance on how to do it. Is there any good pdf for the proofs for multiple linear regression model for matrix alegbra?

$$\mathbf X'\mathbf e = \mathbf X'(\mathbf y -\mathbf {\hat y})= \mathbf X'(\mathbf y -\mathbf X\hat \beta) =...$$

$$=\mathbf X'\left(\mathbf y -\mathbf X (\mathbf X'\mathbf X)^{-1}\mathbf X' \mathbf y\right) =\mathbf X'\mathbf y -\mathbf X'\mathbf X (\mathbf X'\mathbf X)^{-1}\mathbf X' \mathbf y$$
$$\mathbf X'\mathbf y -\mathbf X' \mathbf y = \mathbf 0$$