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minimization a matrix

I have a problem in minimization of the given matrix 

\[Sigma]M[\[Rho]_, \[Phi]_] := 
 Cosh[2 \[Rho]]/
  2 ({{1 + Tanh[2 \[Rho]] Cos[\[Phi]], -Tanh [
        2 \[Rho]] Sin[\[Phi]] }, {-Tanh [2 \[Rho]] Sin[\[Phi]], 
     1 - Tanh[2 \[Rho]] Cos[\[Phi]]}})

\[Tau][\[Alpha]_, \[Omega]0_, t_, r_, \[Rho]_, \[Phi]_] := 
 Det[At[\[Alpha], \[Omega]0, t, r] - 
   Ct[\[Alpha], \[Omega]0, t, r] 
    Inverse[(At[\[Alpha], \[Omega]0, t, 
        r] + \[Sigma]M[\[Rho], \[Phi]])] 
    Ct[\[Alpha], \[Omega]0, t, r]\[Transpose]]
where , \[Rho] >= 0, 0 <= \[Phi] <= 2 \[Pi]}, {\[Rho], \[Phi]}] where as At & Ct are depend on real number constants. I would highly appreciate it if you could write me any comments on how to minimize the the determinat of the matrixa \tau

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