Matrices & Determinants · Matrix equation with integer entries

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:

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