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When the Matrix object is const, or when you are accessing the Matrix object through a const reference or a pointer to a const Matrix.

Yeah, though it may be better to have the const version return a const reference.

Notice that there are two versions of operator().

It sounds like you need to const overload operator(), i.e.,

float& Matrix::operator()(const int nRow, const int nCol)
{
return m_pfMatrix[nRow * m_nColCount + nCol];
}

const float&...

Your copy constructor and copy assignment operator should have the parameter as const Matrix&. After all, it should make sense to copy a matrix that is constant.

I notice that the copy assignment...

That does not really make sense. The destructor will not normally be called from the constructor.

On a hunch: did you implement the copy constructor and copy assignment operator?