Let a and b be real numbers, and
$$f ( x ) = a \cdot \ln x + b \cdot x ^ { 2 } + 3$$
The equation of the tangent line drawn to the graph of the function at the point $(1, f(1))$ is given as $y - 2x + 1 = 0$.
Accordingly, what is the product $\mathbf{a} \cdot \mathbf{b}$?\
A) $- 18$\
B) $- 16$\
C) $- 12$\
D) $- 8$\
E) $- 6$