Proving partitioned matrix involving conditional inverse

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Homework Statement



For matrix X partitioned as [tex]\underline{X}[/tex] = [ [tex]\underline{X}[/tex]1 [tex]\underline{X}[/tex]2 ] with [tex]\underline{X}[/tex]1 matrix full column rank rx,

Homework Equations


prove that [tex]\underline{X}[/tex]([tex]\underline{X}[/tex]'[tex]\underline{X}[/tex])[tex]^{C}[/tex][tex]\underline{X}[/tex] = [tex]\underline{X'}[/tex][tex]_{1}[/tex]'([tex]\underline{X'}[/tex][tex]_{1}[/tex][tex]\underline{X}[/tex][tex]_{1}[/tex])[tex]^{-1}[/tex][tex]\underline{X'}[/tex][tex]_{1}[/tex]


The Attempt at a Solution


I would like to, but I don't have an idea how to solve this problem. I hope somebody can help me here.
 
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