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V a r ( β − β ^ ) = ( X ′ Ω − 1 X ) − 1 X ′ Ω − 1 ϵ ϵ ′ Ω − 1 X ( X ′ Ω − 1 X ) − 1 = ( X ′ Ω − 1 X ) − 1 X ′ Ω − 1 Ω Ω − 1 X ( X ′ Ω − 1 X ) − 1 = ( X ′ Ω − 1 X ) − 1

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\begin{eqnarray*} \mr{Var}\left({\bbeta }- \hat{\bbeta } \right) & =& (\Strong{X} ^{'}{\Omega }^{-1}\Strong{X} )^{-1}\Strong{X} ^{'}{\Omega }^{-1}{\bepsilon }{\bepsilon }{'}{\Omega }^{-1}\Strong{X} (\Strong{X} ^{'}{\Omega }^{-1}\Strong{X} )^{-1} \nonumber \\ & =& (\Strong{X} ^{'}{\Omega }^{-1}\Strong{X} )^{-1}\Strong{X} ^{'}{\Omega }^{-1}{\Omega }{\Omega }^{-1}\Strong{X} (\Strong{X} ^{'}{\Omega }^{-1}\Strong{X} )^{-1} \nonumber \\ & =& (\Strong{X} ^{'}{\Omega }^{-1}\Strong{X} )^{-1} \nonumber \end{eqnarray*}
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