// INITIALIZE VARIABLES
double[,] identity= new double[3, 3];
double[,] inverse = new double[3, 3];
double[,] original = new double[3, 3];
original[0, 0] = 1970.8937129336348;
original[0, 1] = 950.2643718955394;
original[0, 2] = 68.593866605156848;
original[1, 0] = -717.567202536722;
original[1, 1] = 1679.1060115738908;
original[1, 2] = 1237.0289481009058;
original[2, 0] = 0.31232455601872822;
original[2, 1] = -0.21461017714273767;
original[2, 2] = 0.92541657839832714;
for(int row_index = 0; row_index < 3; row_index++)
{
  for(int column_index = 0; column_index < 3; column_index++)
  {
     inverse[row_index, column_index] = original[row_index, column_index];
  }
}

// COMPUTE INVERSE
int success = 0;
alglib.matinv.matinvreport report = new alglib.matinv.matinvreport();
alglib.matinv.rmatrixinverse(ref inverse, 3, ref success, ref report);
if (success != 1)
{
  throw new Exception("Failure to solve for inverse.");
}

// CHECK RESULTS
ablas.rmatrixgemm(3,
        3,
        3,
        1.0,
        ref inverse,   // 3 x 3
        0,
        0,
        0,
        ref original,   // 3 x 3
        0,
        0,
        0,
        0,
        ref identity,  // 3 x 3
        0,
        0);

for(int row_index = 0; row_index < 3; row_index++)
{
  for(int column_index = 0; column_index < 3; column_index++)
  {
     if(row_index == column_index)
     {
       if(Math.Abs(identity[row_index, column_index] - 1) > Math.Pow(10,-6))
       {
            throw new Exception("Inverse multiplied by original does not give identity.");
       }
     }
     else
     {
       if(Math.Abs(identity[row_index, column_index]) > Math.Pow(10,-6))
       {
            throw new Exception("Inverse multiplied by original does not give identity.");
       }
     }
  }
}