Prove That Under the Extended Least Squares Assumptions the OLS $\hat { \boldsymbol { \beta } }$

Essay

Prove that under the extended least squares assumptions the OLS estimator $\hat { \boldsymbol { \beta } }$ is unbiased and that its variance-covariance matrix is $\sigma _ { u } ^ { 2 } \left( \boldsymbol { X } ^ { \prime } \boldsymbol { X } \right) ^ { - 1 }$