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void InvertMatrix( Matrix * theInvertedMatrix, const Matrix * theSourceMatrix )
{
   Matrix temp;
   if (theInvertedMatrix == theSourceMatrix) {
     temp = *theSourceMatrix;
     theSourceMatrix = &temp;
   } 
   
// теперь инвертируем Гауссом и.т.п.
   ....
}

Matrix M = ...
...
InvertMatrix(&M, M):

void InvertMatrix(Matrix& theInvertedMatrix, const Matrix* theSourceMatrix=NULL)
{
   if (theSourceMatrix && theSourceMatrix != &theInvertedMatrix) {theInvertedMatrix= *theSourceMatrix;} 

// invert matrix  theInvertedMatrix

}

void InvertMatrix(Matrix& theInvertedMatrix, const Matrix* theSourceMatrix=NULL)
{
   const Matrix* src;
   if (theSourceMatrix && theSourceMatrix != &theInvertedMatrix) {
     src = theSourceMatrix;
   } else {
     src = new Matrix(theInvertedMatrix); //copy theInvertedMatrix
   }

// invert matrix
// use src instead theSourceMatrix

  if(src != theSourceMatrix) {delete src;}
}

   Matrix src;
   if (theSourceMatrix && theSourceMatrix != &theInvertedMatrix) {
     src = theSourceMatrix;
   } else  {
     src = theInvertedMatrix;
   }