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<tex>\hat{X} = X \times \Sigma^{-1/2}</tex>
<tex>\dfrac{\hat{X}^T\hat{X}}{n} = \dfrac{(X * \times \Sigma^{-1/2})^T * \times (X * \times \Sigma^{-1/2})}{n} = \dfrac{\Sigma^{-T/2} * \times X^T * \times X * \times \Sigma^{-1/2}}{n} = = (\Sigma^{-T/2} * \times \Sigma^{T/2})*\times(\Sigma^{1/2}*\times\Sigma^{-1/2}) = I * \times I = I</tex>.
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