Let $\mathrm{S}=\left\{\mathrm{A}=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]: a, b, c, d \in\{0,1,2,3,4\}\right.$ and $\left.\mathrm{A}^2-4 \mathrm{~A}+3 \mathrm{I}=0\right\}$ 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: