Take $(X'X)^{-1}X'CX(X'X)^{-1}$ where X is an nxn matrix and C is an nxn matrix of ones.
If I could rearrange C somehow then I could use the fact that $(X'X)^{-1}X'X(X'X)^{-1} = (X'X)^{-1} $ to get an easy simplification. Is some sort of rearrangement possible?