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For example i want to have following equation : 

Det[A B C]=Det[A] Det[B] Det[C]

What is the simplest way to distribute automatically?

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  • $\begingroup$ Are you aware that you need . for multiplication of matrices? $\endgroup$
    – gwr
    Jan 18, 2019 at 18:52
  • $\begingroup$ @gwr yes just did not want it to look like ABC as one matrix. basically A.B.C $\endgroup$
    – user49047
    Jan 18, 2019 at 19:06
  • $\begingroup$ Det /@ # & @@ Det[A.B.C] gives Det[A].Det[B].Det[C]. Is this what you want? $\endgroup$
    – egwene sedai
    Jan 18, 2019 at 19:42
  • $\begingroup$ or, Distribute[Det[A.B.C], Dot] $\endgroup$
    – egwene sedai
    Jan 18, 2019 at 19:46
  • $\begingroup$ none fx = RandomReal[{0, 1}, {3, 3}] cx = Det[[email protected] ] Det[fx]*Det[Transpose[fx]] $\endgroup$
    – user49047
    Jan 18, 2019 at 19:52

1 Answer 1

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Try 

det[x__Dot] := Det /@ Times @@ x;
det[x_] := Det[x];

Now

det[A . B . C] == Det[A] Det[B] Det[C]

returns True.

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