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How can I have Mathematica show me also the inverse matrix of the similarity matrix of JordanDecomposition of a matrix?

Obviously I need to use here the Inverse command, but I don't want to manually after using the JordanDecomposition to write Inverse[s], is there a way to extract both $s$ and $s^{-1}$, without using the Inverse command?

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    $\begingroup$ No, not possible. $\endgroup$ – Daniel Lichtblau Apr 29 '16 at 17:59
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If this is for convenience, then you could write a wrapped for JordanDecomposition, e.g. something like this:

Clear[jd]
jd[m_] := Module[{s, j},
  {s, j} = JordanDecomposition[m];
  {s, Inverse[s], j}
 ]

Then for example:

a = {{27, 48, 81}, {-6, 0, 0}, {1, 0, 3}};

jd[a]

(* Out:
{
 (* the similarity matrix s *) {{3, 18, 2}, {-3, -9, -(1/4)}, {1, 2, 0}}, 
 (* the inverse of s *)  {{1/6, 4/3, 9/2}, {-(1/12), -(2/3), -(7/4)}, {1, 4, 9}},
 (* the Jordan decomposed form *) {{6, 0, 0}, {0, 12, 1}, {0, 0, 12}}
}
*)
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