Let \(S={\left[\begin{matrix}a & b \\ c & d\end{matrix}\right]:a,b,c,d\in \left{0,1,2,3,4\right}\) and \({A}^{2}-4A+3I=0…

Let \(S={\left[\begin{matrix}a & b \\ c & d\end{matrix}\right]:a,b,c,d\in \left{0,1,2,3,4\right}\) and \({A}^{2}-4A+3I=0}\) 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:

[JEE Main 2026, 4 Apr (Shift 1)]