Show that if (mathbf{X}^{prime} mathbf{X}) is in correlation form, (boldsymbol{Lambda}) is the diagonal matrix of eigenvalues of

Question:

Show that if $\mathbf{X}^{\prime} \mathbf{X}$ is in correlation form, $\boldsymbol{\Lambda}$ is the diagonal matrix of eigenvalues of $\mathbf{X}^{\prime} \mathbf{X}$, and $\mathbf{T}$ is the corresponding matrix of eigenvectors, then the variance inflation factors are the main diagonal elements of $\mathbf{T} \mathbf{\Lambda}^{-1} \mathbf{T}^{\prime}$.

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