Let $$S = \left\{A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} : a,b,c,d \in \{0,1,2,3,4\} \text{ and } A^2 - 4A + 3I = 0\right\}$$ be a set of $$2 \times 2$$ matrices. Then the number of matrices in $$S$$, for which the sum of the diagonal elements is equal to 4, is :

A

$$20$$

B

$$17$$

C

$$21$$

D

$$19$$