Error component three-stage least squares. Verify that GLS on the stacked system (7.21) and (7.23) each premultiplied

Question:

Error component three-stage least squares. Verify that GLS on the stacked system (7.21) and (7.23) each premultiplied by $\left(I_{M} \otimes \widetilde{X}^{\prime}ight)$ and $\left(I_{M} \otimes \bar{X}^{\prime}ight)$, respectively, yields the EC3SLS estimator of $\delta$ given in (7.25) (see Baltagi (1981b)).