101. Let X be an $n times p$ matrix such that X = [X, X], where X...

101. Let X be an $n \times p$ matrix such that X = [X₁, X₂], where X₁ is $n \times p₁$ and X₂ is $n \times p₂$ and $p₁ + p₂ = p$. Show that a c-inverse of X'X is given by

$$(XX)^{c} = \begin{bmatrix}

X_{1}^{'}X_{1} & X_{1}^{'}X_{2} \\

X_{2}^{'}X_{1} & X_{2}^{'}X_{2}

\end{bmatrix}^{c}$$