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## Main Question or Discussion Point

Starting out a Lin Alg class - my prof wrote this on the board.

(ABC

On the right hand side, I get why D is D, why A and B are now both transpose, but why is C still inverse? I know the rule (D

(ABC

^{-1}D^{t})^{t}= DC^{-1}B^{t}A^{t}On the right hand side, I get why D is D, why A and B are now both transpose, but why is C still inverse? I know the rule (D

^{-1})^{t}= (D^{t})^{-1}, but I do not see how the heck it applies here or what would make the original equality true.
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