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@(@\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }@)@
Determinant Using Expansion by Minors: Example and Test

# include <cppad/cppad.hpp>
# include <cppad/speed/det_by_minor.hpp>

bool det_by_minor()
{     bool ok = true;

     // dimension of the matrix
     size_t n = 3;

     // construct the determinat object
     CppAD::det_by_minor<double> Det(n);

     double  a[] = {
          1., 2., 3.,  // a[0] a[1] a[2]
          3., 2., 1.,  // a[3] a[4] a[5]
          2., 1., 2.   // a[6] a[7] a[8]
     };
     CPPAD_TESTVECTOR(double) A(9);
     size_t i;
     for(i = 0; i < 9; i++)
          A[i] = a[i];


     // evaluate the determinant
     double det = Det(A);

     double check;
     check = a[0]*(a[4]*a[8] - a[5]*a[7])
           - a[1]*(a[3]*a[8] - a[5]*a[6])
           + a[2]*(a[3]*a[7] - a[4]*a[6]);

     ok = det == check;

     return ok;
}
Input File: speed/example/det_by_minor.cpp